Jacketed bullets foul the bore in a different way than lead bullets (cast, swaged, etc). The fouling consists of traces of the bullet jacket material (copper, nickel, steel, whatever). Those metallic traces can be more difficult to remove than any amount of leading deposited by unjacketed bullets. Generally speaking, solvents are required to remove those metallic deposits, and hard scrubbing by bore brushes can be required.

Lead bullets (cast, swaged, etc) can also leave deposits in the bore, but those deposits are far softer and more easily removed than heavy metallic fouling. Usually all that is required is a few strokes with a dry bore brush followed by solvent-soaked patch and dry patches to remove most deposits.

So, yes the jacketed bullets are likely to leave less lead fouling, but removing the fouling of the jacket material can be more difficult than any degree of leading removal.

Also, bore fouling by some jacket metals can have a serious effect on accuracy unless completely and properly removed.

Finally, bore cleaning and maintenance tends to be far more wearing on the firearm than any amount of normal use. Even when properly done with good quality tools and equipment, cleaning up and removing jacketed bullet fouling can cause more wear and tear on the firearm than extended use with other types of ammunition.