Definitely not. If one company checks, it could impact your prospects at other places in your area.

Second others on the experience and certs, certs, certs. These are what got me

Tailoring your resume to the job description and asking good questions in interviews goes a long way in my experience, as well. E.g. “what would you most value?” (referring to certs, knowledge) and “how can I be a better candidate?”

If it’s a company I want to be working for, they’re going to be hiring for attitude above all. Otherwise, if they’re looking for someone plug-and-play they’re desperate to hire, and may be understaffed or facing other internal difficulties.