The mic will pick up audible noise from the relay clicks, and also electrical noise from arcing at the relay switch contacts, unless great care is taken to provide acoustic screening and electrical screening/suppression.
A directional mic might help. Also it could perhaps be mounted on a plastic/rubber foam pad and have a tubular sound-absorbing shroud. That shroud could itself have a grounded metal foil shroud to provide electrical screening. Unless it gets hot the relay could also be enclosed in sound-absorber and screening foil. A snubber should be connected across the relay contacts and all wiring to the relay should be as short as possible.