No in fact it makes the tone better! A blend pot (which is actually 2 pots) or two volume controls are in parallel which means that instead of the usual 500K or 250K volume ohms you now have much lower ohms which loses some brightness. Plus I find that like all 2 pickup basses a mixture of two pickups gives you some scooping of your tone. A simple switch eliminates all that. Push-Pull on the volume control saves you having to drill for a switch.
On my jazz basses I like to have a rotary switch that goes Neck only, both in series, both in parallel, bridge only, mute. I wouldn't recommend that for a PJ, however, because the pickups usually aren't as balanced as in a jazz bass. But you never know until you try it.
The only problem I have with what you suggest is that when In jazz pickup mode, it's only a bridge pickup and for me it takes a bit of EQ to get the tone jazz-bass like the way I want it. This means there's more adjustment than just switching back and forth. My PJ is set up Vol/vol (used 500K to make it more like P bass Ohms when in parallel) and push-pull on 1st volume switches P-bass pickup from series (normal) to parallel which balances better with J pickup and gives a brighter tone so that the combo is more J-bass sounding.
Just try some things and see what you think. Volume controls with push-pull switches are cheap!