Yes, according to the manual, page 20, the FX output on the mixer is before the internal effects processing, so you may use that output as an AUX too.
You could perhaps free up the other AUX send by using the 2TRK Out option for recording instead.
Also, if you don't mind the mix being mono, there is a pretty neat trick: use L for the P.A. and R for the recording. This way you will not take up any aux/sends etc. and you will still be able to adjust levels differently (because it is likely that you will be compensating for the stage sound level on the P.A. mix)
Here is a passage on that from the manual (page 24):
Using L and R in church sound A method popular with some small to
medium sized churches is to use the L fader to control a mono “Live”
mix for the house reinforcement, and the R fader to adjust a
“Recording” mix for the ministry tape. It enables the operator to
easily carry out both jobs with one console. The channel PAN controls
are used to make adjustments between what is heard by the congregation
and what is recorded to tape. This method offers several advantages
which are described in detail on the JdB Sound web site: