It certainly can. Although each regional may have specific factors that affect their hiring strategy, if the airlines at the top pull back hiring significantly then there's significantly fewer people leaving the regionals for the majors. If there are LCC's like Spirit with many pilots leaving then that cuts into the attrition rates at regionals also. The pain flows downhill.

I know the pain is already being felt in a big way by 1500-2000 hr pilots who can't get 121 interviews.

The crazy hiring tsunami is over, and regional FO's can't expect to go directly to majors like they were in recent years. The more normal pathway of having to upgrade to Captain and build some PIC multi turbine are likely here again for most of us... if we can actually win the lottery of being in one of those monthly classes of 30 from a pool of several thousand qualified applicants and get a regional CJO.