Would probably be fine. You are correct that the minimum thread engagement should be at least 25mm here.
The general formula for determining allowable stress is P=S*A, with P=load, S=tensile strength of Al, and A=tensile stress area.
For an internal thread this area is defined as:
with n=threads per inch, Le=length of engagement, Dsmin=minimum major diameter of the external thread, Enmax=maximum pitch diameter of internal thread.
350kg is a mass, not a load. Presumably this is pure tension with no shock loading, thermal loading, etc, so your load would be (9.81*350) N; divide by 12 to find your load per bolt and make sure that's less than the allowable load by looking up the yield strength of Al-6063, the necessary internal & external thread dimensions, and using the above equations. I'll leave it up to you to confirm.
This information can be found in Machinery's Handbook.