This is one I actually haven't attempted too far.
Short answer is: yes, but it is not fun.
There would only be a few places where it would be possible to level up easily, as most of his time involves specific enemies with set exp values. However, I can think of two places off the top of my head it should be doable. First possible spot I know would be his dive into the heart sequence-- you get a save after arriving and then there are about 9? dusks before the door to Twilight Thorn (I believe it was 9, my count might be slightly off). These 9 respawn if, instead of fighting the boss, you turn around and head back to the save spot. I did this to get a few extra potions and things, but it should theoretically be possible to fight those same 9 dusk endlessly until you reach level 99.
The other place to potentially do it would be the very final day as Roxas when the town is filled with Nobodies, or in the mansion itself just fighting up and down the rooms before going through the door to fight Axel.
Again, I haven't really done this-- the highest I ever got Roxas I /think/ was maybe level 20-something? (so, nothing spectacular). I always preferred Sora so I inevitably got bored and quit spam leveling so I could unlock him. Honestly I don't really see the point to leveling Roxas up to an extreme degree here, unless you REALLY like playing as Roxas. Because fighting those 9 dusks in the dream sequence over and over again really sucks, and by the time you unlock the more varied sets of enemies it is the final day so...not much use you are going to see out of it as Roxas specifically and again, I would rather fight as Sora personally. I mean, I guess you can super kick Axel's butt I suppose if that is your thing.
If they let you dual wield that entire final day, boy would that change things, but too bad.
So, yeah, it's possible. There are absolutely no locks on levels, the game doesn't suddenly have Roxas stop leveling or force you to the next cutscene, it just takes a really really long time (we are talking probably a longer time than it would take you to just beat the game outright, so huge time investment) and it's honestly not that fun. It's a grind for sure. Personally I liked the Destiny Island grind more (as you asked about in your other thread about Sora) because there is actually quite a lot to do to mess around on the island when grinding gets boring (like kicking Riku's butt for the thousandth time, or racing him or collecting 99 coconuts or something), but with Roxas he is either stuck in an empty dream sequence, alone, or trapped in an empty town with enemies and...that's it.
I mean, I guess you can do skateboard train surfing in the town plaza if you haven't locked yourself into the mansion yet. (aka, doing skateboard tricks on top of the moving tram while trying to not fall off the top) but now that I think back I honestly can't remember if the tram is even operating on Roxas' last day. Hmm...
If you were REALLY insane, I suppose you might be able to level up fighting the bees. I never considered trying that because oh my god how tedious and awful would that be?
What would be the point of getting Roxas to level 99 anyway? I know one guy leveled Sora up to 100 in KH1 just to prove that it's possible, and I think some of Sora's attacks in that one are unlocked through levelling. I don't think it's the same with KH2 even though I levelled up Sora to 99. I think I forgot ;^^
Just to do it? I dunno.
I know I personally enjoyed having a save file where my characters were ridiculously over-leveled at early game points just because it made playing through the story easier when I didn't really want a gameplay challenge and instead wanted to watch the story. It came in handy when I was trying to introduce a friend of mine who was very much a non-gamer into the series so she started up the game on my level 68 destiny islands save file and basically just smashed everything in no danger while still feeling like she was "playing" the game. Got her into the series so, no regrets there.
It's obviously not so much a thing people might do now-adays because you could always look up the cutscenes on youtube or watch a lets-player but that wasn't really a thing back when the game just came out, so having a "god mode" file was useful for that reason.