In general, you would never inject water into a GC-MS as it would damage most columns. Also, samples should be run in either the solvent they were extracted in or a very similar solvent to make sure that they dissolves properly for the analysis. So always solvent extracts for GC-MS.
Never use water in the GC MS which is gas chromatography which is used for the volatile compunds such as essential oils, while the LCMS can be used for nonvolatile compounds.
Just to clarify something that often seems to crop up on these type of questions. An essential oil is not a single compound, but a complex mixture of compounds, many very volatile, others less so. Essential oils are extracted from plants by distillation. Any other method of extraction does not produce an essential oil, although some of the same compounds may be present in an essential oil and a solvent extract for example. It is true that GC-MS is quite good for essential oils, but many of them are so volatile that headspace is needed to capture them as they are lost during solvent extraction and analysis by conventional GC-MS.
The answer to your actual question remains the same - never put water in a GC-MS as it will destroy your column. You should really read up on GC-MS analysis if you are thinking of using it. There is a lot of information on the web: manufacturers such as Agilent have lots of useful information on their websites for example. There are also many good textbooks about GC-MS.