Yes. A rocking toilet grinds the wax seal underneath it a little more every time somebody sits down, and once that seal fails water goes into the subfloor rather than the drain. Shimming it solid is a twenty-minute job; ignoring it is how bathroom floors rot out.
Why a small movement is a real problem
The toilet does not bolt to the drain. It sits on a compressible wax ring that seals the gap between the bottom of the toilet and the drain flange in the floor. Wax has no memory — every rock squashes it a little further out of shape, and it never comes back.
When it finally fails, the leak is under the toilet where you cannot see it. It soaks the subfloor, usually for months. By the time the floor feels soft or the ceiling below stains, you are replacing subfloor and sometimes joists, not a three-dollar wax ring.
Fix it properly, and do not just tighten the bolts
The instinct is to crank down the two closet bolts. Do not. Porcelain is brittle, the base is thin at the bolt slots, and over-tightening cracks it — usually a week later, usually while somebody is on it. Snug is snug.
The correct fix is shims. Plastic toilet shims, pushed into the gap on the low side until the toilet does not move at all, then trimmed flush with a knife, then caulked around the base. If the gap is more than a few millimetres your floor is out of level enough that it is worth asking why.
Should you caulk all the way around?
Yes, but leave a gap at the back. Caulking the full perimeter is required by code in most places — it stops mop water and worse getting under the toilet where it cannot dry. Leaving a two-inch gap at the rear means that if the wax ring ever does fail, the water appears on your floor where you will see it, instead of being sealed in to rot the subfloor quietly.
When it is not the shims
If the toilet still rocks after shimming, or the floor around it flexes when you step on it, stop. Soft floor around a toilet means the damage is already done and there is water in the subfloor. Shimming a toilet onto rotten decking just delays a bigger repair.
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