For large stage productions this is the standard procedure. The mic signal is split twoways or often three ways, some times four ways: on-stage mixer (doing the sound on the stage), audience mixer, recording, TV send.
It is basically simply splitting the signal into several paths. No problem with signal strength, the input impedance of a standard microphone input is high enough to not effect this.
A professional splitter normally has a transformer inside. The reason is not to modify the sound, but to solve a completely different problem -- ground loops. All the different mixers has their own ground connections (through the mains) and this may get you into a trouble where currents goes through the ground lead. This may in itself not be a problem, but it can induce mains hum into the signal (50 or 60 Hz). Typically in a stage production there is a lot of lighting that creates a lot of electrical noise as well. So the professionals goes for transformers.
You do not need to go for a transformer as long as ground loops does not turn up to be a problem. Maybe your equipment is battery powered, not even grounded or you are close enough to the mixer and with little enough electrical noise going around.
I would create a simply Y-cable, ask for permission and be clear that if a problem occurs it is allowable to cut my recording out of the chain -- audience first. Just be certain that your equipment is phantom power "aware", the soundboard might output phantom power on all channels so your equipment should not choke on that.
// gunnar