Can I grow a snap pea vine up a youngish cherry tree?

I have a three or four year old Vandalay cherry tree that I am thinking of growing a snap pea vine up.  The tree is about 5 feet tall with a 2.5" trunk diameter at it's thickest. Why not use it as a trellis?  Maybe given that the pea would be allowed to flower and fruit it will suck out too much N? Maybe the tendrils of the pea will strangle the tree branches?  Maybe once the tree leafs out it will block out the sun to the pea vine?
Has anyone done this?  I can't tell if it is a bad idea or a good idea.  Googling produces zero results.  
Thank you from the PNW.
(Oh and the crows eat all the cherries off this tree, but leave the other two cherries trees alone.  It is my gift to them for sparing the others).

I don't think you have to worry about the pea eating all the good stuff and the cherry starving. I would hope the cherry's roots go way lower than the pea's. And it definitely won't choke the tree with its tendrils- you'll be ripping it out in a few months while the cherry will stay.
a 5-foot tree should be fine. I would plant maybe 4 or 5 around the tree, in fact!!
Good luck and welcome to the forums!

Thank you Tereza!  I am going to do it!
I can't believe it has taken me this long to discover this forum!  I look forward to reading all the shared knowledge and experiences!