Benny,
Yes, no problem, you can turn on the source or preamp while the amp is on without too much problem. There is a small click, but it's not significant and not damaging in any way.
The output of the GK1 is capacitively coupled to the amplifier via a 1uF Auricap. At switch on, the tube is cold, and no current is flowing through it. Consequently, at the instant of switchon, the voltage across the Auricap is 0V; as the filament warms, current flows from plate to cathode and through the cathode resistor, whose voltage then begins to rise to about 48V. This voltage rise starts at about 6 seconds, and is finished by about 12 seconds, with most of the rise occuring in the last three seconds. This rise of 16V per second is not so great that it causes problems for the power amplifier, so the answer to your question is that it's quite OK to leave the AKSA power amplifier on and switch the preamp on and off on demand. You will hear a click, but it's not damaging, and very quiet.
Cheers,
Hugh