SP foliage and stems are pretty scruffy and are not particularly pleasant to look at despite the lovely flowers. They are also prone to mildew. They would try to climb rather than trail and you'd end up with a tangled mess IMO. However, there are dwarf and bush varieties suitable for container growing which would give you the flowers and you could add something else for the trailing element.

Here is a link that might be useful: Dwarf sweet peas

That's funny you ask, the one and only time I tried Sweet Peas I also planted them in a window box figuring that if they could climb, they could drape :) That was not the case, and it was a disaster...

I haven't tried sweet peas since. There was a thread about a week or so ago about sweet peas and varieties. I would search for it. Among variety suggestions, there was a bit of talk on draping versus climbing and why sweet peas don't cascade very well.

In short, I think they tend to grow up, not down, and would be much better planted in a place to climb.

I planted a trailing nasturtium in that same window box the year after and that one was lovely. Draped beautifully and flowered on and off for a long time. I wa smuch more pleased with that ... and when I try sweet peas again, I will let them grow upwards.