Depends on the ooze. A gelatinous cube which just engulfed you? Sure (you're treated as grappled but don't fall prone when engulfed). A black pudding? Nope.
By the rules, you couldn't, I'd let you, but trust me, you don't want to. If youwillingly entering a critter like that, i'd say you walked into the grapple and would be now occupied with keeping the thing from eating you too badly.
I agree with Shilsen. It depends on the ooze. Some oozes can 'engulf' in which case I'd say you can voluntarily allow yourself to suffer the effects of an engulf.