IMO, only if reaching the cam-in-question is VERY difficult to get to.
If not, I'd leave the cam mounted and try cleaning the cam end of the RJ-45 female in the pigtail as best as I could, dab some dielectric grease in it and substitute a really long patch cable from the cam to your POE switch/NVR to see if it'll come up...then take it from there.
Taking the cam down is best for safety and thoroughness...I know I tend to be rushed when I'm teetering, hanging on one-handed plus swatting flies, bees and wasps.