If the bamboo poles are the thin ones sold in garden shops, they probably won't be strong enough. It will depend upon their exposure to wind - once loaded by vines, a strong gust could snap the bamboo & bring the whole trellis down. If they are a sheltered location, they might be OK. My recommendation would be to add more poles, or anchor the whole structure to something solid.

What kind of peas are they?

I was thinking the same thing. Yes they are pretty thin bamboo, and though they are pushed into the soil about 18", the soil is so fluffy in those beds that it wouldn't take a lot to shift them. My yard is relatively sheltered with woods on two sides, but occasionally a storm comes through that does some damage. I am going to beef up the trellis this morning.

Half the row is Oregon Sugar Snaps and half the row is Sugar Ann.

I am behind this year - but excited to finally get a few things in the ground!