Do these things have any measurable influence on survival rates?

yes.

To expand on yes:

They prevent attack via numerous herbivorous creatures and whipper snippers.

They prevent them from getting eaten when young, don’t they?

prevent them form getting eaten
provide a favourable microclimate

party_pants said:

prevent them form getting eaten
provide a favourable microclimate

They even do quite well in terms of flood protection.

Conceivably they also provide protection from ‘igh breezes.

They’re completely useless in the face of Bogans in 4WD utes with a pig dog cage on the back of the tray, but will protect against uneducated volunteers who are supposed to be removing weeds.

BTW, if they’re yours, talk to your local council about free mulch for revegetation projects.

I had always wondered about these things. Quite often I have seen dead plants covered with plastic after the bamboo stakes had moved or disintegrated. Those using them should remember to come back and check them regularly and remove them when it’s time to.