No, that's not possible. mIRC uses the standard Windows DNS functions (a part of winsock), and those always use the nameservers configured in Windows.
Instead, you could use for example nslookup.exe if it comes with your Windows installation - combined with /run, that is. Or (shameless plug) you could use my
nslookup script that implements its own DNS client in mIRC-script. The list of DNS servers that it uses, is part of the configuration.