Yes you can do it in less time, but as UCaggie has said, it depends...
Very tough to do it in a reef tank that quickly if you are also adding corals, fish, etc. If you take a bare-bottom tank and add seasoned-live rock (REALLY seasoned - like 1 year or more out of the ocean) and don't add fish, corals, other inverts, so that you ONLY have a BTA... you can do it faster.
It all comes down to bio-load and established bacteria colony. A BTA (by itself) will not generate a huge bio load unless you are feeding it heavily.
This assumes you have all other conditions optimal - like lighting, high oxygen levels, protein skimming and water movement.