The main problem with porting DOSBox to the Amiga would be, from what little I know of programming, the source would probably need major rewrites.
The main power of the Amiga was delegation of function. It's unique chipset allowed different functions to actually be handled by dedicated chips acting as their own processors. It was also a lot more efficient with memory management than even today's PCs. 99% of the games, for example, would run just fine with a measly 1meg of memory installed. As a matter of fact, most of those would run well with only 512k of memory installed. The exact same game on a PC, in many cases, required 8meg or more of memory. Also, games that ran just fine on a stock 7.5mhz Amiga 68000 CPU (with much of the graphics, sound, math, etc... functions out-sourced to other chips,) ran slugishly on even a 33mhz 386 system. My stock A2000 consistently out-performed (over all,) my PC until I first upgraded to a Pentium computer. Even then, my stock A4000 still outperformed my PC (over all,) until the P3 came out.
The problem is, that this is only the case because those same programs were basically re-written to take advantage of the Amiga's unique chipsets. Because DOSBox's main usage requires it to function with 100's of games, I just cannot see any way that it could be altered to do the same. On the other hand, I see no reason whatsoever why it could not be compiled to take advantage of a PPC accelarator. It would not run at all on a stock Amiga, but by using the PPC processor, and if it could be written to out-source at least some of the functions, it should run rather well.