Not normally. Normally the throat profile is ground into the finish reamer. You could get one made with no throat, like a roughing reamer, or else with a minimum throat with no freebore, then get a separate throating reamer made, but it's quite an investment and it is usually more economical to adjust your loads to match a standard chamber geometry.
The neck portion of a chamber reamer can also be altered per special order, as many custom rifle makers have for clients who are going to outside turn their case necks to thinner-than-average wall thickness. Neck length is usually ten or twenty thousandths longer than case neck maximum to allow for neck pull during start pressure build-up and before the bullet is released, but you could get it made shorter if you were controlling your neck lengths tightly.
I'd suggest you call Manson reamers
and talk to Dave Manson. Describe what you are trying to do and he will know the prudent limitations.