I believe the answer is that it depends on what your samples are like, and what exactly the amino acids are near the ends of your peptides.
The usual problem with y2 ions is that they are not very selective and are therefore likely to display interference from other peptides in your sample that have similar precursor mass and identical y2 ions. Most peptides in your digested sample have a "K" or an "R" on the end, so the y2 ion effectively only provides one amino acid of selectivity.
You can tell Skyline whether to include y2 and b2 transitions by default by choosing different "Product ion selection From:" options at:
Settings > Transition Settings > Filter
While b2 ions are slightly more selective than y2 ions, they are still considered low selectivity ions, and by that we mean they are more likely to encounter interference from other molecules and also to show up in other places than where you molecule of interest actually elutes. Using multiple low selectivity fragment ions can fool a researcher into thinking their coelution is evidence of the molecule of interest, when you are targeting without stable isotope-labeled reference standards.
The b-ions in beam fragmentation are more likely to experience multiple fragmentation events, which I am told can result in very high b2 intensity as larger b-ions fragment again into this smaller form. It is my understanding that Thermo triple quads (and HCD) exhibit this more than SCIEX instruments. Also Thermo CID will exhibit very different b-ion intensities than its beam fragmentation (HCD) because each molecule is limited to a single fragmentation event in CID.
So, yes, it depends. If you are confident in the peak elution time for your peptide (especially if you have a SIL reference peptide) and you determine your small ions are not experiencing interference (e.g. by ratio-dot-product with your SIL reference), then by all means use them if they are intense and nicely coeluting with other more selective transitions.