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It wouldn't effect the accuracy of the frequency and besides you intend to use it with a frequency counter. According to the manual the high output connector would have been used if a radio was in bad enough shape that it would be "deaf" to the normal signal levels. It was not intended to be used with a counter, which would have been a rare beast in 1946 outside of a research laboratory. You can adjust the the frequency fit of the dial using the frequency counter after you get the generator re-capped and running. The RF amplitude is not well controlled on this service grade generator anyway. If you were able to measure the signal strength you would find that it probably varies with frequency across the dial and from band to band.
I would guess the hole for the banana jack is 1/4 to 5/16 inch. The BNC jack I linked to would need the hole increased to 3/8 inch. You could do that with a drill. Stick a lump of modeling clay or "tent" some masking tape on the other side to catch most of the metal fragments. You also could do it using a tapered reamer instead of a drill.
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