Forking seems like a very expensive solution to the problem. Especially in php where exec() doesn't actually do what exec in unix does in general (contrary to plain exec which you'd use after a fork, PHP's exec still runs a shell).

If you use their API even just one time per request, be aware that they will fork, execute a shell, fork again and then execute curl. Imagine where this is going when you use multiple API calls per request.

As this is "just" about analytics, why not use a UDP packet or two? Sure - they might not get delivered, but is that really so bad for analytics? Sending out a UDP package is very fast and there will be no waiting going on at all.