I suppose it's unlikely, but you might also check to see if there is a
hairline crack in the back of the toilet, somewhere, also. Strong
smells would probably be more indicative of a wax problem, as noted,
than through a hairline crack.
An observation and solution: I have a toilet in an unused/remote
area. When I've forgotten about it, the water evaporates from the
bowl, enough for sewer gases to emerge. At times, it had taken me a
while to figure out why the mystery odors seemed to come and go, when
my first thoughts didn't take into consideration this unused toilet,
until I realized what was enfluencing the fluctuations in the odor
prevalence. I discovered the smell was more noticeable when the
outside winds were strong. I, now, try to remember to give this
toilet a flush, occassionally, to catch the problem before it presents
itself. With the absence of an air tight system, mystery odors, as
this, may be more noticeable when the outside winds are up.