In all honesty, with the unit that you have - No.
The Alesis units have the slowest Trigger to MIDI conversion on the market. You can buy a sampler and trigger it from the Alesis unit, but if you do anything more intricate than basic 4/4 stuff at mid-tempo, you will quickly become unhappy with the situation - the faster and more intricate you play, the worse it will get. The only analogy I could come up with, is it's like pouring bb's into a funnel - at some point, no matter how much you pour into it - only a certain amount is going to get through at once.
I tried doing exactly what you are talking about doing, about 10 years ago - when the DM5 (The D4's "supposed upgrade" - I say this because I thought the D4 actually had better/usable sounds in it - the DM5 was like a "dance"/rap type of sound module to me) first came out. I spent $1,000 on an Akai sampler and a DM5 and was utterly disgusted with the performance. Sure, if I played AC/DC type of stuff it was fine.
So if you don't intend to do anything really spectacular - it will work fine.
Otherwise, save your money and either get
a Roland Vdrum or a ddrum unit.
I wound up going with a ddrum2 (I picked it up used off of E-bay for about $400, and the stock sounds sound exactly like a real drum set - and they are all completely tunable.)
The Alesis unit is really for the keyboard player who wants to add some drum sounds via a rack unit. The Alesis triggering interface is slow to begin with, but when you try converting to MIDI it becomes really obvious.
I have heard people claim to be using a maxed out laptop with a Roland TMI to trigger the sounds in Drumkit from hell, but that may be BS - I haven't actually seen it in person, so I don't know. That would provide you with the ultimate drum sound for live use because you could have unlimited sounds, and could build totally custom sounds - but like I said, I haven't actually seen it done - so it might have been people just pulling my leg.
Tim