Actually ... NO. First, The Colt 1851, 1860 and 1861 were ALL built on the 1851 frame. The 1861 was built on an unaltered 1851 frame. The 1860 was built on a modified 1851 frame. The frame for the 1860 had a rebate milled in the forward water table to accept the enlarged 1860 cylinder. The base area of the cylinder is the same size as the 1851 cylinder. The 1860 chambers stop short of the locking bolt slots.
A key point is the 1861 was built from an unmodified '51 frame and the 1851 cylinder. Look at the ASM "1860" conversion will show an unmodified water table and an unmodified 1851 cylinder. The ASM "1860" Designation is derived from the the Army Pattern, larger grip assembly. The ASM 1860 is actually built on 1861 patterns.
Were you to put the cylinder in a lathe and durn down the back of the cylinder, you would move the socking bolt slot AWAY from the Bolt. There would not only be a very large (ugly) space between the water table and cylinder, the bolt would probably not reach the locking slots at all.
If you absolutely MUST have an 1860 conversion, start with a Pietta 1860 and fit a Gated Kirst Konverter. You won't have a First Model Richards but it will be as close as you can get for less than 2 1/2 or three grand.