You would get caster level +20 on dispel checks.
6th level spell automaticaly dispeling all spell with caster level 19 or less
Empowered Empowered dispel magic could even give 50 on dispel check or (1d20+10)*2 giving 60. Is it allowed?
No. The caster level check is a way of determining the success of the spell, not a random effect of the spell itself. At least, that's how we work it in my campaign, otherwise why would they even have written Greater Dispelling?
You could always make a new metamgic or general feat that gives bonuses to caster level checks, such as dispelling. Or you could just design a "supreme dispel magic" spell.