I would have thought that once on HT, the downside of delaying chemo for a few months is negligible, versus ensuring infection is completely cleared. Indeed, it wouldn't surprise me if chemo becomes more effective as PSA drops lower, for same reasons radiotherapy gets more effective the lower the PSA (where getting down to 0.1 is ideal if you can), but I'm guessing here with regards to chemo. If so, the important thing would be to monitor PSA, and have the chemo before it starts rising. Ask the onco.
Or is the problem that this is a frequent or continuously running infection, and it's likely to be difficult getting a clear duration long enough for the chemo?