When you blow one leg of 3 phase, you have single phase. There is no such thing as two phase. If you have single phase loads, like lighting, etc. you will still have power on those legs, but any three phase loads such as motors will not be too happy. The motors will do what is called "single phasing" and draw excessive currents, stall out, and you should end up blowing distribution side fuses. If you are continually blowing a specific fuse, you should lock out the system until you can correct the cause of the problem, not ask, "Will it work without the fuse."
If you are observing three phase power still on the secondary of the transformer, be aware that if you are running a lightly loaded three phase motor when one leg blows, it may actually generate the third phase which could be backfeeding some other devices on your power system, including the primary side of that transformer.