It matters, but it is no longer something is required to get a call from a Legency carrier with exception to UPS/Fed Ex.

You have FOs with no TPIC getting picked up by Legency carriers, but they are usually Regional FO ~> ULCC/ACMI FO ~> Legency FO.

Usually a recent training event triggers the apps (types, upgrades) along with volunteering, LORs, job fairs/meet & greets.