Connect means to add one part of something to another part. Like two lego bricks. Most people would see 'connect poems' as on poem being added to another at the end. 'Combine poems' would be to mix them together in the way I think you want. Maybe 'combine' is a better verb to use here?

Yes, you could say you create poems with your friend by writing lines that connect with each others'. Or, that the lines you write connect with your friend's lines and that's how you and your friend create poems.

I mean when I say a line of poem (come up with it impromptu, not read from anything), then I ask my friend to say another line, it has to rhyme with my line, then it's my turn. And then it's my friend's turn, until we complete 4 lines of a poem. What do you call this? Connecting poem?

"Continue with another line".

No. Sorry. Can you explain your meaning in another way?