Ionic liquids are per se compatible with ESI. http://pubs.rsc.org/en/Content/ArticleLanding/2004/CC/b314754a#!divAbstract
Ionic liquids and other impurities have also been tested with LC-MS. http://www.dionex.com/en-us/webdocs/85797-PO-Pittcon-IC-MS-05Mar2010-LPN2418-01.pdf
I am not aware of anyone using an ionic liquid such as 1-butyl-3-methylimidazolium hexafluorophosphate as an additive to the LC solvent. Since it will not crystallize, I would suspect it enter my mass spectrometer and coat my quadrupoles rather quickly. I would expect this not to work for very long, but let us know if you find out otherwise.
In my research group, we tried to use ionic liquid such as 1-butyl-3-methylimidazolium hexafluorophosphate, as extractant in sample treatment. However, we observed that the signal was very low. This fact could be attributed that ionic liquids are not volatile. In my opinion, I would not use ILs in MS.
Ionic liquid are compatible with LC-MS but, can because of their ionic nature, suppress the ionisation and sensitivity of MS for your analyte if they coelute or are ionized in paralell. It is beter that ionic liquid, present in sample, is separated from your analyte by HPLC before enter MS detector.