A cover crop is one you plant in the off season or on unused garden beds to keep your soil from eroding or leaching nutrients, and to produce organic matter you can till back in or compost. Do you mean rotating your crops  planting cukes next year where your tomatoes grew this summer?

There are quite a few different recommended cover crops used for different purposes, but all of them are pretty much cold weather tolerant. I do not think that cucumbers would survive long, even in my zone. You do not say where you are from, but zone 4b they would not even last as long as they would here.

I also like edible cover crops, but plant which works well for me. I have also thrown in some seeds for radishes, spinach, carrots and beets a time or two. Usually, the mustard outgrows everything else and crowds the smaller stuff out.

They are usually about knee high a little after the first of the year when I mow, mulch and turn them under along with the other amendments that I put on my garden.
Bill P.

Winter tolerant green manure cover crops for tilling in in the spring are great for your garden and many choices are available. They not only add nutrients but improve the tilth of your soil.

It is all good advice above and I can only add that if you use cukes and if they survive to fruit at all you will have hundreds of volunteers next year - likely where you DON'T want them. ;).

But if what you are talking about in an inter-planting of them (like a ground cover) with your tomatoes and peppers then yes, it will cause you problems. Cuke vines will climb anything and will choke off tomato and pepper stems.

Dave