In fact, when I bought a Dynaco st35 (used) some 35 years ago it came with 12AX7 installed and the circuit was not modified in any way. It worked without any problems. I had the unit a few years and only many years after I sold it I realized the amplifier was supposed to use the other tube - this was before the internet, so information was not so easy to get.
Dynakit / parts.com, still sells the kits, I bought all the assessories with it about 800.00 what a great little amp!!!
If you run the math the phase splitter section has 109V cathode to plate with 3.5mA of current.
Looking at the plate curves this is easy for section two of a 7247 (a 12AU7 like section).
Not so easy for section one (the 12AX7 section), the plate can only pass about 2.6mA at 109V plate to cathode at zero grid voltage.
So the phase splitter section using a 12AX7 tube in place of the correct 7247 tube will be operating with the 12AX7 basically saturated with near zero grid bias.
The result will be higher distortion and power loss in the output stage due to lack of grid drive voltage on the 6BQ5 outputs.
So if by "working" you mean sound will come out with a 12AX7 stuffed in? Yes sound will come out.
If by "working" you mean works to the originally designed performance levels then the answer is, no not so much.
Will you "hear" the difference? That will depend on too many factors to say.
The splitter section is direct coupled, so a little grid current may not be a catsastrophy, but scaling up the split load resistors is easy enough. Plenty of Golden Era amps (H. H. Scott for example) used a 12AX7 to drive a pair of 6BQ5s with long-loop feedback without issue. I'd probably start looking at a plate load of 75K Ohms and scale the other two resistors proportionally (to parallel to 75K). Or even leave out the positive feedback; it's not much anyway.
All good fortune,
Chris
All good fortune,
Chris