no, not necessarily.
It could be end play or gearing on one axle that is the problem, so only binds when axle is sliding out, or when axle speed is higher or lower than the other axle, it could just be higher or lower only not both.
I would jack up the back and check end play on both axles, Fords do have some normally, 1/4"-1/2", more than that would be a concern, even 1/2" could be the start of an issue.
End play is from the C-clips that hold the axles inside the differential, they can start to wear and eventually fail, axle will come out while driving down the road, not a good thing.
Usually this would produce a clunking sound when cornering as axle slides out slightly then comes back in when straightened out, not a binding issue.
I would think side gear wear could cause a binding on one axle.
If possible I would drain the fluid and watch it for metal filings.
Drive around to warm up the oil then drain from the bottom, check for metal, clean off gasket and refill with the old oil if no filings are seen, add some Limited slip oil if needed on your model.
Driving a limited slip differential without the limited slip oil in it will make you think the rear end is going to drop out, lol, so it is very important to have that in there if it is a limited slip differential.
I bought a corvette once that had "a rear end problem", guy had changed rear end oil but didn't put in the additive, started binding going around corners, I got it cheap, expected to put in a new rear end, but all it needed was the additive
