First thing, the tools from the standard toolbag won't be enough, you will need something for the rear axle nut ( 22, and it's not in the toolbag... ).

Then, regarding checking the tension, don't try to do it on center stand because once you get it off, the weight will compress the rear shock and the chain will get extra tension in it. Best way is the one described in the manual, with the bike on the side stand because at least there is some weight compressing the rear shock and the slack indicated in the manual should work for standard load.

If you're riding 2 up and with lots of luggage, on the other hand, it would be best if you check and tension the chain with the additional load on the bike.