That MOSFET has a Threshold Vgs of 1V, that means it begins to switch significantly at 1V.
It's Vgs is specified as +/-20V max. If you were worried about Vgs being 1V, and you were aiming to protect the device, then there is no need to do that, as it is 20V.
No, I don't think you need R22. It has some benefit, by protecting the ATmega2560 pin if you think things are likely to short to ground or power.
But it isn't necessary. The MOSFET gate has a very high impedance (and only 5nC of charge), so you don't need to limit the current, as you would with a bipolar transistor, and the pull-up resistor R21 is huge, so it'll make no difference there.
"I'm pulling the gate to the source voltage to default the switch to closed"
R21 will do that for you if you 'tristate' the ATmega2560 pin. It'll do no harm explicitly driving it high.
Having said all that, you could simply replace R22 with a 0ohm resistor and leave the board as it is.
As Michael Karas wrote, it will likely conduct enough. However, as you can see from the Drain to Source current, it is not fully switched on.
Fig 6 in the data sheet shows the 'flat' on the Gate Charge curve at close to 4V. So it doesn't look fully turned on at 3.3V from that either.
There really doesn't seem much point using that device unless you have little choice. If it is exhibiting enough resistance to limit the current at 3.3V to under 250mA, then it is going to drop more of the voltage for the GPS, which might impact its behaviour, and the MOSFET will warm up, worsening its properties.
I'd look for a P-MOSFET with Rds specified for 2.8V or less.
Looking at IRF, who make other devices in the same micro3 package (and thus avoid redesigning your PCB) they let you search for Rds(on) for parts which switch at 1.8V or 2.5V in the same package, for example IRLML6401, IRLML6402, IRML2246, IRML2244.
You have to add those Rds(on) 1.8V and 2.5V parameters to the search by hand, they aren't there by default.