It depends on what driver you're using.
I assume you mean 4 Li-Ion (Lithium Cobalt or Lithium Manganese Rechargeable) cells which would give 3.7V*4 or about 14.8V. If your driver is meant to work with that high voltage, then it should be fine.
Just for reference, so you are aware of how things work:
The energy of a cell is measured by its capacity*voltage (This is simplified) - but say, a 3.3Ah / 3.7V Li-Ion has 3.3*3.7 = 12.21Wh of energy. So, 4 cells would have a total of 12.21*4 ~ 48.84Wh of energy.
However, an LED only works at a certain voltage range. For 2.8Amps of current, it will need (according to the seoul p7 datasheet) ~3.6volts. If you dump 15 volts into the LED, you'll *poof* it! (This is assuming you'd wire your 4 cells in series)
Now, with power=voltage*current, that's 3.6V*2.8A = 10.08W of power the LED needs.
This means your driver needs to supply 10.08W to the LED, which means that the driver needs at least 10.08W (Of course, in the real world it will be less efficient, so you'll need more).
So if you were using 4x 3.3Ah Lithium Ion cells at 3.7V each, the current running through them would be current = power/voltage = 10.08W/14.8V = 0.68A. At this rate, your cells would have a runtime of 3.3Ah/0.68A = 4.85hours. (You can also calculate this using the 48.84Wh energy from 4 cells - 48.84Wh/10.08W = 4.85hrs) Given inefficiencies - I'd put runtime around 4hours. I've never built this though, so I won't comment.
Regarding your question about nimh/alkaline, under heavy loads, alkaline has very high internal resistance, meaning that its voltage will sag and go down very quickly. Think of it this way: (a) An alkaline starts at 1.5V, but goes down VERY quickly. On the other hand, (b) A NiMh starts at ~ 1.4V, goes down to 1.2V and stays there for a much longer time, before running out of juice.
So, a NiMh is able to deliver a lot more juice than an alkaline.
But you can't really decide on a power source without looking at what your driver is spec'ed for - what voltage input range it accepts.