If you are asking a generic question (i.e., a mutation in region A of a generic GPCR causes gain/loss/change of function), the answer is probably NO. But if you are asking about a specific GPCR, and you are willing to dig and do some legwork, you may find tons of information here:
http://www.gpcr.org/7tm/
This database is maintained by the CMBI in the Netherlands and it is at most a few months behind in the literature.
Here is a website that collates mutations in glycoprotein hormone receptors (Luteinising hormone receptor, thyroid-stimulating hormone receptor, follicle-stimulating hormone receptor). Some of the mutants are described for gain/loss of function characteristics. Otherwise, you could use it as a starting point to search the literature for studies using these mutants.
As an extension of your question, you should also research pharmacological chaperones (See Newton et al. 2011 PNAS for eg.) AKA pharmacoperones. Not only will you find many papers citing mutant GPCRs, but you will also see that many mutants affect functioning not by inhibition of signalling ability, but rather by inhibition of proper localisation of the receptor protein.
One extra point to consider is that mutations very often affect expression level and this alone can affect signalling. Sometimes these effects will be quite drastic in either a positive or negative direction. Although some changes are quite predictable many are not.