That would give me about 350*1.4=490 volts DC after rectification and filtering.
Yes.
If I use the center tap like most marshall amps do, that would give me 175*1.4=245 volts dc.
I'm not aware of any amps that use only 1/2 the winding for HT.
I have a transformer that is rated at 350V (175-0-175) at 60mA center tapped.
The maker is tersely saying this combination of things:
i) if your draw 60mA through the secondary, you will have 350VAC;
ii) this implies that if you draw less than 60mA, the secondary voltage will be higher; if you draw more than 60mA, the voltage will be lower;
iii) if you draw more than 60mA, don't blame the maker if the PT fails.
Does that mean that I get 60ma if I use a bridge rectifier across 350VAC?
No. Current is drawn from the power company, trough the wall socket, and through PT by the load presented to the PT by the amplifier. E.g., if the load = -0- = short circuit, an infinite amount of current will be drawn. Something will burn out, hopefully a fuse. IOW, you the designer control the current draw by way of the load you present.
Would the current capabilities still be 60ma or would it double (since you have two 175 volt windings in parallel)?
Current handling capacity is determined by the gauge of the wiring used in the windings. (In a coil, a wire's current handling gets more complicated, but that's the idea.) If you were to use ea side of the winding for different 175VAC power supplies (out of phase), ea side could handle 60mA.
Hope that helps.