You can do anything you want to June but I wouldn't recommend it as the sweet peas are going to use the clematis as a climbing frame and, depending on which group the clematis is in, you may want to prune when the sweet peas are in flower.

Well I suppose it does depend on the clematis concerned, but by and large, most are not pruned from now till midwinter anyway, so I'd go for it. Might be difficult to deadhead or cut the flowers on the sweetpeas often enough if they're entwined in clematis growth though.