A little photo forensics first.
The photo that Platefire posted looks like what I believe is a Dr Z-made Carmen Ghia. I say that because the wiring and board mounting is just slightly better than the chassis in Sluckey's picture, and the chassis is yellowish. Dr Z used to (maybe they still do) use an aluminum chassis which was given a chromate dip; the chromate gives the chassis the yellowish look. Additionally, the red glyptal marking the turrets which have been completed is something Dr Z did (again, I don't know if they continue to do this).
So it looks like the chassis more-likely to be a Z doesn't have the cap (at least in this one example).
But Sluckey's right. This phase inverter (probably the one I'm least familiar with) is a differential amplifier, or basically a fixed-bias long-tail. There is one grid directly driven by the preamp signal, and normally a large-valued resistor over to the other grid, which then usually has a cap to ground. This circuit needs an input signal which represents a difference between the two grids, as a typical gain stage has an input which is a difference between the grid and cathode voltages. Most commonly, this is done by driving one grid while keeping the other at a.c. ground (via the cap), which then results in a difference between the two grids.
You might be tempted to think the resistor between grids makes both grids see the same signal. Assuming no current flows through the resistor, it really keeps both grids at the same d.c. voltage. The cap to ground then looks to signal like 0v, which you could think of as a voltage divider like a volume control turned to 0.
So with no cap, we have a divider made of 470k and 8.2k. Not the same as a.c. ground via the cap, but that keeps what in-phase signal which does leak to the "non-driven" grid relatively small.
I think all-in-all, losing the cap would make the phase inverter have less gain and output swing. The "right way" is to use the cap. I'd be curious to see how large the phase inverter output is with the cap, and whether it drives the EL84s to overload to easily. Maybe Dr Z wanted to hamstring the phase inverter just a little bit to have more range on the volume control.
The easy way is just to try the amp with and without the cap. If you anticipate building more than just this amp, you can probably find a use for extra 25uF/50v caps hanging around.