2 hour APL 2 adventures give 225-300 XP, but APL 3 adventures (which are more typical) give 450-600 XP. Two such adventures would be enough to guarantee level 3.
Sure, but there are two problems with this:
1) We don't know what levels 5-2 and 5-3 are optimized for, which determines the XP range. If they're both level 2 mods, then the OP isn't going to have enough XP to get to level 3 unless he starts 5-2 at level 2.
2) A level 3 mod is surprisingly dangerous even for a level 2 character, and is outright deadly for a level 1. The more XP might be available from the mods being targeted for higher level PCs, the more likely it is that a level 1 or 2 character won't complete it, and thus won't get any rewards.
I'm not saying it's impossible, but the OP should have a backup plan in the event that his character doesn't complete the modules as expected -- and the backup plan shouldn't be 'pretend I didn't die in the last adventure'.
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Pauper