Never built any speaker cabs...
...but I have done some furniture and cabinets...
I think you shoud be OK. Properly made glue joints are usually stronger than the materials you are joining. You could drill pilot holes in your bracing and screw them(carefully) to the cabinet sides...or use biscuits(but you need the tool)...or use locking mitres(but you will need the proper blades and tool)...
Again, I'm no expert in speaker cabs(or much of anything else, for that matter), but most folks seem to use MDF(including manufacturers) and then either paint or veneer them...less resonance and such. Ply may be OK, but the layers can de-laminate under some circumstances...check out some kit sites, find out what they use...hopefully there is someone out there who can provide some insight on that issue.
As a side note, cutting and fitting veneered ply can be an absolute b!tch...you always run the risk of porking up the edge...unless of course you have a workshop and skills like Norm Abrams(and I've seen some questionable things even from him). Most of what I have done required building and then veneering...it may seem as though you are saving a step by using faced material, but in the long run I have found the two-step porocess a bit less taxing on my patience. Using a good quality veneer and contact cement, you can even bookmatch the woodgrain exactly. This could even eliminate the need for mitre cuts...
jimHJJ(...good luck...)