No.
The 12-volt CT winding (6-0-6v) can deliver about 0.5 amps RMS current; the 12AT7 consumes 0.15 amps so there is 0.35 amps to spare. That's about 4.4 volt-amps.
The center tap must be grounded since this winding serves as an electrostatic shield for the 2.5v windings. Are you thinking perhaps of generating a +/-12vDC supply for some other circuit? If so, that could possibly be done.
Thanks for the info Paul. I am going to install a LDR volume control in my Stereomour chassis, if the current transformer could handle it that would save me a small transformer, since it can't I will simply purchase the transformer as well.
Best,
Ed