A distance of 20 bp in DNA (I assume) has a length of 68 Angstrom. This should be close enough for a significant extent of FRET quenching by BHQ-1.
The behavior of FAM in this system could be surprising. It is likely to be at least partially quenched already due to interactions with the DNA, regardless of the BHQ. If the oligo is denatured, its fluorescence intensity could increase. In other words, for certain uses, the BHQ may be unnecessary.