Does changing web hosts (changing a domain's nameservers) affect the private nameservers / glue records created under that domain?

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http://serverfault.com – We currently have a virtual dedicated server with GoDaddy and have 4 domains under it. I ended up creating private nameservers under, say mydomain_a.com, and have ns1.mydomain_a.com and ns2.mydomain_a.com as the nameservers for the other 3 domains. Now, we're thinking of switching web hosts (not domain registrar just the host) which means I have to change mydomain_a.com's nameservers to the new host. Will that affect or mess with the other 3 domains still pointing to ns1.mydomain_a.com and ns2.mydomain_a.com? Will that affect the private nameservers / glue records in anyway? (HowTos)