The floor should be pitched so that water would run to the pit. If that is so, in order to move the pump you would need to install a floor drain at that location with a drain line to the new pit.

It does not sound like a real sump pump.

It is being used as a condensate pump.

You are going to have to extend all the lines that empty into the pit presently to the new location.

lazypup...the floor is indeed pitched to the current sump and I fear drilling new drain line will be super expensive and very disruptive. Not sure it's worth it?
brickeyee...you have described it perfectly. My fear is the day we need a true sump if we move it and don't have a replacement option. But with no drain tile feeding it, the basement would have to be flooding from somewhere else, right? (windows? upper floors? something catastrophic...)

Thanks.