Am I able to get any type of NETA cert without being employed by a NETA sponsored company?
No, you must be employed by a NETA certified company to be eligible for NETA certification.
If you obtain the cert at a NETA company and leave that company, the certification will carry over to another NETA company but will not be valid at a non-NETA company.
There are also some continuing education requirements to keep the certification up to date. Check out the NETA ETT standard for more details: ANSI/NETA ETT - InterNational Electrical Testing Association