Yes if it is used in parallel resonance mode. You can then theoritically
tune it down to the serial resonance frequency (a variation of a couple of
KHz for a MHz range crystal) by increasing the loading capacitor. No (or
very little) if it is used at its serial resonance. But 99.9% of the
CMos-based crustal oscillators are parallel mode.
You can also shift it by putting a capacitor in series with the
crystal. This leads to a better oscillator in most cases. The
circuit looks like this:
Y1
C3 !-!
From amplifying device -------+-----!!----! !----+--- To amplifying
device
! !-! !
=== C1 === C2
! !
GND GND
The ratio of C1/C2 is constant so that amplifier needs a nearly
constant gain. Changing C3 changes the total capacitance seen by the
crystal.
"No problem" may be the wrong answer here. How stable do you need the
resulting oscillator to be? When you pull a crystal, you do suffer
some reduction in stablity because the capacitor's value matters more.