I'm pretty sure that you can. But it also probably depends a lot on the heat sink itself.
I've seen a P1-166 running without a fan, but the heat sink was rather large. (Large for such an early chip.)
Where as my own P1-133 has a fan on the heat sink, but the heat sink itself is very small. So I know I'd never try to run that one without the fan because I couldn't trust the heat sink to dissipate enough heat alone.
So if you think the heat sink without the fan is large enough to actually cool the chip, then go for it.
i've got a k6-266 with a heatsink, no fan, although the heatsink is about the size of the one on my tbird- anyway- it runs just fine, however, the pentium and k6 is probably like comparing apples and oranges, i just felt like putting in my 2 cents.
You can buy a new fan for $5 at a fare if you're worried.
I read about this guy who didn't like noise, so bought a new K6-2 550MHz (not very common these days) and set it, on his old motherboard, to 3x50MHz from 5.5x100MHz, so it ran at 150. This was cool as ice, and ran even without a heatsink (for a short time). I think you could make ice cubes by placing a cup of water on the chip's die (j/k).
I guess manufacturing processes really do improve. (this story is not certified. I agree it probably ran fanless, but without a heatsink? Hmm...)
~ I'm not AMD biased, I just think their chips are better. ~