Not by your own definition.
Yes, in fact, it would. The problem with attempting to hyphenate Conservatism is that the principles it stands upon are interactive, interwoven.
As an instance, you can claim to want small government, but that is impossible without fiscal conservatism reigning it in, and welfare will be predictably rampant without imbuing Christian moral principles...
The inter-operation of Conservative principles requires each the other. Some guy once said something like:
'Our Constitution was made only for a moral and religious People. It is wholly inadequate to the government of any other'So the Constitution, in and of itself, without the Judeo-Christian prism to interpret it through, will fail. I will assert the same is true with regard to all Conservative principles... Because that is what American political Conservatism seeks to preserve. All of it is needed.