Is there any benefit to tripping a GFCI receptacle when it's not in use?
TLDR: Being energized isn't what kills outdoor GFCIs. The weather is. Put 'em indoors and protect the (plain) outdoor outlets using their LOAD feature. 

The "TEST" button is not intended as an "off" switch. Edit: except this one is designed for that purpose.  Tripping the device when not in use might help the internal electronics avoid surge/spike damage. Might, depending on which side of the interrupt the electronics are on. 

However, for an GFCI device kept in the mean outdoors, that is the least of your problems, as discussed elsewhere.  The small amount of heat from the GFCI may help ward off condensation.  The best way to extend the life of a GFCI is move it indoors. 

Almost all GFCI devices, including "receptacles", are able to grant GFCI protection to additional devices.  You can put one of those indoors somewhere earlier in the circuit, and have it grant GFCI protection to the rest of the circuit, including the outdoor receptacle. That becomes a plain receptacle with a "GFCI protected" sticker.  Test using a 3-light tester which has a GFCI test button.