Does using a snapshot of running PID on Linux provide enough entropy?
No, it doesn't; not unless you want to have $2^{15}$ bits of non-cryptographically secure random token - the output of the $RANDOM function of bash.

How PID's are created depends on the operating system. The only other information is the starting time really. Neither of those can be seen as random and is easy to guess and even to influence.

There have been some proposed patches to make PID's more random in Linux but they were rejected by the kernel maintainers. They are kind of chicken-egg anyway; to create random ID's the kernel would need to have a good random number generator which you could employ yourself.