I made a filter box once out of acrylic and weld-on. After adding a few extra braces and such it does indeed hold water, but its the ugliest thing you've ever seen.
Just a word of caution - welding with acrylic is hard to do pretty. Yes, it is a chemical bond and holds REALLY well, so yes if you get good coverage it likely won't leak, but unless you have experience its harder than it looks to come out nice looking.
I'd also be curious to see your budget. When I did the math it really didn't save much money at all to build it myself since you pay so much for acrylic sheets, I figure the aquarium builders pay WAY less than you would, hence they have a decent profit margin. What my original plan when I started building the filter box was to get into it as a sort of side business, and I'd try to get my sheets of acrylic from Midwest Custom Acrylic scrap / misc piles (I don't know what they charge, but I figure it'll be cheaper than new and I'm close to drive there and pick it up so free shipping), but it was such a pain I didn't bother....yet...still may try...