If you do not mind the appearance that unpruned clematis often take on........bare, woody bases with flowering growth restricted only to the uppermost portion of the vines......then your plan should work. Be advised that many pruning group I clems (and some group III's) are very vigorous species that may easily outgrow and overwhelm the small growing LFH's, so space accordingly. Generally the advice NOT to combine various groups is due to difficulties in pruning individual vines but if one elects not to prune at all, that consideration is eliminated. However, the different growth habits and vigor of the various groups may be a limiting factor.

I'm a confirmed rebel, gardengal :-) Nothing ventured, nothing gained... From your comments, it doesn't sound like there are any 'deal-breaker' concerns. I'm not concened about 'bare legs' because there is stuff under/near them to hide most of it. Root competition with other things will be an issue - I expect some of the clematises will not survive/thrive because of competition, and not great soil on the house side. I have over-planted (just finished that today) to start with on the assumption that there will be attrition in the ranks one way or another!

Clematis seem to grow well here and I quite like the group 3s I have left unpruned - they actually seem to do better than if pruned. This is the arbour and gate that is at the front (facing the driveway) end of what will become the clematis swag. The Jackmanii Superba in the picture below picture had never been pruned and it was planted in 2002 or 2003! It certainly got pruned this past week when DH cleared the New Dawn roses - and everything else - off the arbour and swag:

July 2 2010:
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July 12 2010:
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The back side - you can see some of the swag chains... They extend ~20' down each side of the alley, so there are 40' of chains plus 8' across the width of the arbour. My objective is to have that covered in cascades of clematis for as long as possible during the growing season.
June 23 2010:
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July 12 2010:
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Here's another view of some unpruned group 3s on the other side of the house. The ones on the chainlink fence are 4 years old and have not been pruned other than to remve a bit of top growth in spring. The ones on the copper-pipe fence get accidently pruned - usually at the wrong time of year! - by the dogs when they are bouncing around, complaining about being left behind in the backyard when we go through the gate into the front yard!
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The group 1s are on planted to cover the top of the arbour and spill down the front to join the spring display in the gate area:
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So, I'm not terribly worried about unpruned group 3s clematis becoming too unsightly - and I like vigorous! :-)

I thought I'd do an update on how the clematis swag is progressing... I've been surprised at how vigorously some of the clematises planted last summer are growing. The ones on the house side (the sunnier side) are growing - not surprisingly - MUCH faster than those on the fence side (shadier side). The old Jackmani Superba that got cut back hard when we took down the roses has come back very strong. I do prefer the look it had when it cascaded down from the top, so it'll definitely be left mostly unpruned so it'll be able to do that again. There were Montanas on the arbour before too - they don't bloom a lot most years but I like them. I didn't expect them to survive the cutting back process last summer, but they did and even produced a couple of flowers this spring. So things have been going well so far and I have high hopes that the swag will become a very pretty feature in the garden. A few pictures... :

The arbour and gate last night:
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Looking through the gate - you can see end of the swag on the house side:
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The top of the arbour from the pantry window a week ago - there are more flowers there now:
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A few Willy at the end of May:
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Some Gillian Blades in early June:
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Some Galore at the begining of July - I really like this one. It's very vigorous and still blooming a lot.
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The gate end of the swag on the house side July 4th. The Black Prince clematis is another one that I really like.
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I'm not sure which clematis this is but it's pretty :-)
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Here you can see that the fence side doesn't have much growth at all. That picture was from a couple of weeks ago - there are now some clematises on the fence side that have reached the swag chains and have buds on them so should be flowering soon.
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So I'm very pleased with the progress and looking foward to a bigger show next year - assuming the drought we're in doesn't end up killing everything!

Looks wonderful. Hope the drought isn't too bad. Lack of water really hurts Clemmies.

We've only had 1 mm. of rain since June 24th! I have a soaker hose along the house side but we have to hand water the fence side since it was set up to be watered by the overflow from a rain barrel - that's not effective when there's no rain! At least the shade helps reduce how often they need to be watered.