Hi
normally recent static mat have >10 meg and up ,so in theory it safe to let a PCB powered and on the mat
(for some time mat have go from conductive to disipative for safety reason typical spec was Surface resistivity is 10^8– 10^9 Ohms. )
but ideally try to avoid it ,since even if it safe it may affect circuit behaviour
but old mat may much lower
and mat must be connected to EARTH whit supplied cable ,most of time in that cable it put for safety a 1 meg resistor