Do I need to replace the fuel pressure sensor of a 2007 Volvo XC90 V8 AWD?

We don't do price/shopping questions here. To get an idea if $525 is a reasonable cost for replacement, ask another mechanic or another dealer in your area.

Did you see the "check engine" light illuminated, or has it merely been reported by the dealer? Erratic or incorrect fuel pressure would certainly trigger the "check engine" light, and may generate poor engine running or no running at all.

If you delay the replacement, the car may run poorly or the engine may stop running. It's unlikely, however, to be further damaged. It certainly will not pass an MOT or DMV or emissions review if they're called for in your state or country by the re-registration or sale of the car.