This is what I know about my laptop:
HP Pavilion g6
Processor: Intel Core i3 M370 @2.40GHz [I'm told this is a quad core. I guess that's good?]
RAM: 4.00 GB (3.80 useable)
Win 7- 64bit
Graphics Card: Intel HD Graphics
Approx. Total Memory: 1696 MB
My system maps very closely to yours. I have a dual core i3-2310 system, which is the next chipset after your core i3. I'm using integrated graphics as well, but I think the hardware revision mine is at had a graphics boost. I also have 4 GB of memory and am running Windows 7 64-bit.
Will I be able to install and use the MGE?
I had no problem with MGE, but trying to run any of the shaders (as outlined in the MGE section http://http://knotstheinane.blogspot.com/p/morrowind-modding-guide.html, which I recommend) pretty much immediately made the performance drop to unusable levels. This was after all the environment texture packs though.
Running MGE XE yields okay results (again without extra shaders), but frame rates can drop below 10/second in some areas (Balmora, heavily wooded areas). It does look nice though, the shadows are a nice touch. Even so, I'm considering going back to vanilla MGE sans shaders (or playing with the shaders some more to see if I can find a nice middle ground) for the performance.
You may in fact have better performance with MGE XE than me, regardless of video chipset, as I see little to no difference in MGE XE when running fullscreen 1600x900 compared to 1024x768, so it may be CPU limited, in which case your extra cores MAY be useful (although morrowind apparently can't take advantage of extra cores).
To save you trouble now, here's a tip that's stated everywhere but I can't overstate the importance of: right click and go into the properties, compatibility and set to run as administrator morrowind, morrowind launcher, MGEgui, MGEXEgui, morrowind code patch and anything else related you might run as an application/executable. For a while I through MGE XE (and the latest MGE subversion build) wouldn't work on my system, but I had forgotten that step...
Edit: I just tried MGE 3.8.2 r0178 again, and disabling all AA and other filtering, no shaders, I'm getting ~18-20 FPS in a scene I get 14-15 with MGE XE. I'm thinking MGE XE is worth it.