I too use plastic cups. I do not like the peat cups. They dry out too fast.D.V. is there any particular reason you're using plastic cups? I bought several packages of peat-pots from our local dollar store (small, but 25 or so in a pack for $1 - I was happy!) and then I'm able to transplant the entire pot out into the garden with out disturbing the seedlings at all.
Yes, you can plant the whole peat pot, but your plants would like it better if you broke it off when planting. I had some peppers in peat pots one time and after planting out, they were not growing. Finally I dug some up and the roots had not penetrated the peat pot, so the little plants were pot bound.
OK, that is two reasons I don't like peat pots.