Is it technically possible to convert it to Li-Ion? Sure, given the time and money.
AFAIK, "some" newer Dewalt drills have some of the battery management electronics in the tool itself, or maybe I am only thinking of the battery power level indicator. Regardless, yours being NiCd or NiMH, will not have this suitable for Li-Ion packs.
The Imax charger cannot do anything about protecting against discharge because that happens disconnected, in the tool during use. If you run any cell in the pack down below 2.(n)V during use of the drill, you will likely ruin it. You can measure the current your drill uses, perhaps it's not a lot since it is only 12V, but that it's a good contractor grade brand may work against you.
My old 14.4V Dewalt, is VERY strong for being only 14.4V, stronger than a typical $100USD Li-Ion drill you'd buy today. Apparently they used high current motors at the time, as it might have been a higher tier product with 18V not very common yet.
The point is, I'm pretty sure that mine draws more than 10A current, probably 20A is closer. 5A does not seem like enough margin. To put it in perspective, a mid-grade drill may have around a 350W motor. If you have 3S Li-Ion cells so 10.8V nominal, at 5A that's only 54W.
Converting a drill to Li-Ion is easy to write
I want to, but the particulars, especially when it's a lower voltage drill, without the right charger and no protection board (yet) can make it less desirable than just buying new sub-C NiCd or NiMH for it (whichever the original charger supports).
Consider that there are now Low Self Discharge, sub-C NiMH cells in the market. Whether your charger can do NiMH, I don't known as you never mentioned its model # nor even that of the drill, but since they are LSD cells, it would be less work and less fiddly to use it, with the main downside being that the pack would weigh a little more than if you had stuffed 3 x 18650 Li-Ion cells in it.
On the other hand the up side to that is you can use 10 sub-C cells and have a 12V drill again instead of a 10.8V drill.
http://www.farnell.com/datasheets/1655619.pdf