I'm assuming you're saying you will apply to the transfer school, but before you are accepted or rejected, you want to do the write-on competition?
If so, I guess it depends on the school and how many spots they leave open for transfers. If you have time and don't care about wasting a lot of it, I don't see why not. I personally wouldn't bother, especially if there were only 3 spots or something like that, and I didn't have my acceptance letter in hand yet.
My guess is the real craziness would be adding that on to your summer work plus your own school's LR competition. Another craziness factor is if you figure there's a 10% chance of getting onto LR at the transfer school, and then factor into that equation all the uncertainty about whether or not you'd get in there in the first place, then you're devoting an enormous amount of time to a tiny chance of getting any real benefit.
But, hey, it ultimately comes down to what you want to do. I personally wouldn't even think of sacrificing a second of the time I'd otherwise devote to my own school's write-on competition (no true grade on, everyone has to write on
) or summer work to another school's competition. But if you're firmly graded onto your own school's publication, have a few weeks free before your summer job starts, and are one of those insane type-A people who would rather be doing a write-on competition than chilling by a pool or in a bar, then all the power to you. It'd be a crazy great bonus to snag a rare transfer spot on a preftigious journal.
TL;DR: No bright-line rule; apply a case-by-case, fact-based analysis