Voltage drops when turn on electric fan

Adding the relay will add a little bit more drop actually.

If this is 12v at idle I wouldn't worry about it.
If it's 12v max with the fans on something is wired to lightly and it can't get the amps through it that it needs to keep up..
^^^ Yes, rev it up to 1500 or 200 RPM and see what the voltage does.