I was just wondering, since I'm decided to tune my bass(SR500) down to C indefinitely, should I give my truss rod a slight adjustment to compensate for the fact that there's less tension from the strings, or should it do alright? At this time, my string gauge will remain the same.
Leave it a day or 2. Then you should see if you need to adjust it. Also remeber the phrase, 'If it ain't broken, don't fix it'. Meaning if it plays fine don't adjust the truss rod because you can cause more problems and permanent damage.
^^ what he said
You might want to raise the action slightly.
if the strings buzz a lot against the frets maybe give it a little tweak. then after that tweak try the action. looser strings will vibrate more widely.
i had to for mine, i left it in drop C for a week, in my cold shop, and the neck bent way back, so i had to loosen it a little.