Htoo, consider yourself lucky....that you have both VGA and DVI sockets.
If one should stop working.....you have the other one, to fall back on.
But, yes, you can connect/use both....at the same time.
I did it...out of curiousity, saw little difference...in monitor's resolution quality.
On my monitor, the 'default setting' worked... for both cables,PZ.
(This depends on your the quality...of your Monitor, actually.)
Left the VGA cable 'in place'...so I would know where it would be, if I ever needed it...later.
(Yes JC, but the monitor would use only one input or the other. Having two connected is handy but doesn't affect the image. -PZ)