Funny you should ask, and the answer is no.
Believe it or not, putting a MOV across the contacts on the timer that controls the solenoid drains the surge off much slower and doesn't cause the imbalance that the surge causes, I have played with a few caps that results in the same effect or better.
To understand the reason why inductive kick back causes cheap GFCI's to trip goes back to the time when GFCI's were first coming out, even as late as the mid 1980's many manufactures didn't put much filtering to filter this spike out as well as the small time delay that today the chip in a GFCI looks at the imbalance before taking action, this time delay was the most effective way to stop most inductive trips as the speed of the spike was very short duration and had a fast rise time and decay, this put a high frequency ring into the load side of the GFCI that since it would be out of sync with the 60hz it would cause a current to develop in the sensing coil (current transformer) of the detection circuit that would cause the electronics to trip the GFCI, this high frequency pulse caused by the inductive kick back is what trips the cheaper (China made) or older GFCI's but this pulse last a very short period in time, and the National Semiconductor LM1851 chip found in most newer and better made GFCI's including breakers has the gated delay set to the max that UL specs allow which I think is 25ms which is about a half of a cycle at 60hz but is effective for most type of inductive kick backs.
It is hard to design a LC circuit to filter out this high frequency pulse because the LC circuit would have to be design where it doesnt place the dump current on the load side of the GFCI, it's not the high voltage spike that one might think is the problem and is why the MOV has little effect on the problem, it is the high frequency of the spike that is the problem, and is the same reason why many of the newer florescent lights that use 25hz to help light the lamp can cause problem if the GFCI manufacture doesn't include any filtering for these higher frequency loads.
A near by lightning strike which is also a high frequency event can also trip GFCI's even if it doesn't damage the GFCI, I have come home a couple of times after a storm has gone through to find that most of my GFCI's are tripped, but the reset and test just fine only to find out later that lightning had struck a tree a couple doors down.
Attached is a good paper on GFCI's the goes into a little about the problem with HF, but if you click on the links to the LM 1851 chip you can read a little about the gated delay in the specs.