It's highly unlikely that most synthetic cannabinoids will be tested for or are even available for testing. To my knowledge, this is part of the reason they continue to be produced in the first place. The longer cannabis and it's related compounds remain illegal = more 'noids that avoid legal jurisdiction and drug tests. Only a few labs test for 'noids and usually this is only on request and for the most popular ones such as JWH-018.
However, this is not to say it's impossible to test for them. It's just that nobody has the time to sit there and identify the metabolites of hundreds of coumpounds... that will be obselete by the time their work is complete. A slight variation on a chemical's structure can change it's entire metabolic path, the properties of the compound and it's metabolites. RC producers take advantage of this and will continue making these slight variations into the infinite realm of cannabinoid structures. This can be seen with all drug classes - MXE, etizolam, 25i-NBOMe, MDPV, BZP, etc. probably wouldn't have made it far out of the laboratory if it weren't for the help of prohibition. Yet somehow society continues to ignore this perpetually-worsening damage it inflicts on itself. Yes, I use synthetic cannabinoids. Why? To avoid losing my freedom to the imposed "consequences" of cannabis use... I'm sure many have the same reasoning.
Anyways, this has turned into a bit (a lot) of a rant and I will attempt to actually answer your question now. Assuming the lab has the knowledge and equipment to test for a particular cannabinoid, the high fat solubility common in that class would likely mean it would stay in your system for quite a while. I'd say 3-5 weeks as an educated guesstimate. However, due to the vast array of cannabinoid compounds nobody can say for sure... better to just assume they won't be tested for. That's what they were invented for, anyways.