Hi!

My question is simple: if I put Endeavor in Raddus' pocket, does it get to gain her contain?

Nope. Once set aside, it can not trigger any of its cards or be affected by any cards. Raddus-tucking ships can also prevent them from gaining objective tokens and such from certain Objectives as well.

Thanks!

FAQ, p. 8:
Q: If a ship or squadron was set aside and is deployed at the start of a game round by an ability or upgrade card effect, can it resolve abilities and upgrade card effects at the start of that round?
A: Yes, as long as those abilities could be resolved at the start of the round in which that ship or squadron was deployed.

My interpretation is if you pull out Endeavor at the start of the first round, you may gain the contain. Otherwise, no.

Yup, if its "set aside" at start of first round, No token.
If, as Bertie said, it is deployed at start of first round, you deploy it with Raddus, you could then gain the token.