I think this is a bad idea. The gold contact is the most
durable (esp. in terms of long term contact resistance)
you will find. Anything like tin will oxidize over time and
need scrubbing to keep bright, leading likely to test
unrepeatability.
Now you might want to look at what "mating" means.
A solder joint under the wrong conditions could
consume a thin gold plating layer (a not uncommon
problem in microelectronics assembly) or vice versa.
But a simple short term physical contact, is not
going to have the energy to make these chemical
changes. The only issue would be whatever is on
the "lead free finish" (which is pretty nonspecific,
otherwise). Pure tin and high tin concentrations
can grow whiskers but this is not the pogo pins'
problem, but a board materials problem.
If I were you, and you weren't driven to the
absolute lowest cost construction (i.e. no gold
was on the PCB) I would think about making the
board test points have gold on them. Gold-gold,
problem solved. But it's a cost adder. The
engineer's question is, how does that cost
compare to test repeatability and test escapes
related costs?