2009 Honda Civic LX with 160,000 miles. It’s only getting around 9-15 mpg. It has a check engine light for purge flow, emissions. I could run my machine on it again. P0497 is the one I remember top of my head.

A mechanic replaced the purge valve solenoid. That didn’t fix it. Another mechanic claims it’s a bad/clogged vapor canister and it’s been a month trying to get the part.

Could a vapor canister really equate to the bad MPG/fuel economy?

 

If the purge valve is working correctly than NO. That is the only part of the system that will effect MPG.
Here's the thing. If the MECHANIC just replaced the valve without testing the system the new valve may be compromised.
If the canister is gas logged it likely expelled pellets into the system and they get into the new valve and meed it up RIGHT AWAY.
They should have replaced the canister and BLOW out the lines to clear them.