Is there an issue with me changing location to where I want to work and explaining to recruiters that I'm not currently living there but will be?
That will depend on each recruiter and if they decide they like that or not. A recruiter may think you actually live some place and go through interviews, etc., only to find out that you don't actually live there. This may be disappointing for some recruiters that did not wanted that to happen, and could be a waste of their times.
Personally I would not do so, as it may be a bit deceiving for my taste, specially if you put a place that you actually are not thinking on living, just with the hopes to get a work there and then be relocated.
However, I see no problem doing what you say if you actually are going to or had lived there recently. Have in mind that Linkedin is a Social Network (or tool) for you to expose yourself in the professional world. As in any Social Network you are in complete freedom to post the information you want regarding what you wish to obtain from it, just try to do it with care.