Unfortunately this is quite complicated and there is no clear consensus on if it is better to enrich or which enrichment technique is best. So the answer is “Quite Possibly” sometimes this works and sometimes it doesn’t. Not very satisfying I know…
I’ve seen cases where not enriching can generate better data and I have also seen cases where enriching phosphopeptdies will lead to an identification of a phosphorylated peptide that was missed without enriching.
Here is a recent paper That compares several phosphopeptie enrichment techniques.
The Association of Biomolecular Resource Facilities (ABRF) recently did a study on identifying phosphoylatied peptides. You can see the results here
It’s quite interesting, so it’s worth a read.