Yes. You can put together a 1911-pattern pistol in much the same
fashion as you would an AR/M4 clone.
However, almost all 1911 aftermarket components are deliberately
manufactured slightly oversized and need to be trimmed and 'final
fitted' by the builder. This gives the builder the option of
assembling as 'tight' or 'loose' a 1911 as he desires.
'Tight' 1911s are built to extremely precise tolerances to maximize
accuracy. However, they can be very finicky about the type of ammo
that is used, and might jam if they are not fed the right ammo or
kept fastidiously clean. 'Loose' 1911s, on the other hand, are
built with reliablility in mind. They can be fed a wide range of
ammo (e.g., round-nose, hollowpoints, truncated cones,
semi-wadcutters, etc.) without jamming, and can continue to
function even when they get dirty. However, the loose tolerances
that enhance reliability result in degraded accuracy.