Is the speedometer and A/C somehow connected/related?

My speedometer is out and my A/C is not blowing cold. Someone said if I fix one it might fix the other by saying it's something to do with the instrument cluster. You think this will work? 2004 Ford F-150 Lariat

They might run off the same module. I'm not a mechanic though. Go to the Ford F-150 forums and ask.

I very much doubt they are related.

No. Fix the speedometer first. You do not want to get a ticket for speeding.
Check for codes with a scan tool. If you are not having problems with the transmission, it is likely a bad cluster.

Fix the AC next. What is wrong with it? Check if the compressor clutch is engaging when you turn the AC on. If it does not, check for power at the coil connector and check for good compressor ground with engine running and AC on. Power and ground is good, the clutch coil has failed. Power is not present, replace the AC relay. Still no luck, it is time to see an AC shop with gauges.

I doubt they are related.