This is probably just plain dangerous to the rest of your system.
It would depend on "giving a kick" at turn-on, provided that the
power supply had a rapid rise time. If the fan ever gets stalled
in normal operation the kick is not there, and the thing just sits
and encourages the rest of the system to cook.
What I'm suspecting is that if a cap were in parallel, a
bypass for the power to the fan, it would just make matters
worse because whatever the turn-on delay was already, adding
more capacitance will only lengthen that delay.
Ric wrote about it being parallel with the resistor though,
so i presume actually paralleled to it, bypassing it on the
same power lead. While that can be a crude but effective
filter for some noise reduction, I'd not heard of anyone
employing anything like this for fans.
Sometimes it's not even, merely a matter of getting the fan
to spin-up though, with some fans there will be pulsation
below a certain RPM, actually making the fan louder than if
it were running slightly faster-enough to eliminate this
pulsation. Offhand I'd speculate that it pulsating occurs
due to stronger (permanent) magnetic field in some fans than
others. IE- It seems more common in >= 120 x 32mm, large
thick fans.