Do you need high water pressure to use a gas powered pressure washer?

No. Typically a gas pressure washer will use less water volume than if you turned your garden hose on full blast. The pressure washer does not depend upon water pressure, but it does need decent volume so be sure to turn your hose faucet to full open once connected.
Normal house line pressure of 45-50gpm should work for most residential size pressure washers.
A simple test would be to track the time it takes for your garden hose to fill a 2 gallon pail when opened fully vs the same time it would take to fill the bucket with your pressure washer. OK, maybe that second test is not so easy as the pressure will keep knocking the bucket over. Be safe now.