What is the impact of disabling a printer's checkbox for "SNMP Status Enabled" with or without a print server inline?

The impact would be mainly driver- and model-dependent. You will lose functionality like the ability to automatically retrieve the printer's installed options or meaningful error messages upon print job failures or holds. Also, some printer drivers come with client-side applications reporting ink/toner status - this would typically be unavailable as well if SNMP is disabled for the print queue.

Also, as joequerty pointed out, the printing functionality itself is using a different protocol and would be unaffected.