Theoretically, no. The power tube and speaker's sensitivity rating determine how loud the amp is. Having said that, you may get more perceived loudness due to the extended highs and lows of the beefier OT. But again, the speaker can only reproduce sound in its bandwidth. You're not going to get thunderous lows out of a 6" speakers.
BTW, the speaker really is a limiting factor in bass response. I used to run a Silverface Champ into a 4 ohm 4X12" cab and had no problems getting massive amounts of bass out of that little 5W circuit.
I did a quick check on the net and found that the Eminence Alpha 6A is a 6", 8 ohm speaker. It has a sensitivity rating of 93 which is a lot less than the 97-100 of most speakers. It is also rated at 100 watts
I wonder if it would fit in that cabinet?
tung