I know that if you put a fridge on it's back for transportation you're
supposed to leave
it for 48 hours before turning it on (to let the coolant settle or
something). What I want
to know is whether I can tip it, say 20-30 degrees, and plug it in again
immediately
without any problems.

One trick that gets them working more quickly after disturbance is to turn
them on for ten seconds and then off for a few minutes and repeat many
times. This runs the compressor enough to distribute the oil, but without
overheating the unlubricated bearings.

Given that it will only be tilted a little, just a bit of care turning it
back on should be OK. Don't sue me for a new fridge if it mangles itself.
Definitely at your own risk.

Christian.