Will this UGF set up work?

I have a 2 1/2 gallon rectangular aquarium which houses one male
Betta. I have been looking for a way to filter it for him....I know,
high maintenance fish...but he particularly likes this tank. Tried an
internal filter, he freaked and wouldn't move for days so I removed
it. I'm not too fond of a sponge or corner filter idea. I just
purchased a one gallon hex tank and was going to use that UGF system.
The tank measures 6 W X 12 L. The filter plate (in the shape of a
triangle) measure approx. 4 1/2 W (at it's widest point) by 7 L. The
riser tube looks perfect, being about 2 inches lower than the height
of the tank. Question...For one fish, will this set up work?  I
remember reading that an UGF does not have to cover the entire bottom
of the tank (I think it was referring to a fry tank) and wonder if
proper filtration will be provided if the entire bottom of the tank is
not covered. I vacumn and do a 30% water change on my other filtered 2
gallons weekly and will do the same here.

And just one more quickie...Would this scenario work? Fishless cycle
in the one gallon....then transfer all over to the 2 1/2 gallon
(water, gravel, ornaments, UGF, etc., no rinsing) and consider that
almost fully cycled? I ask, as again, he is easily stressed by change
and would not want to move him to a smaller tank while his is being
cycled.

Hope this cloudy head is making sense!! 

Thanks for any input!