The encoding part can fail if the server load is too great?
Yes, it can fail if your server is on high server load. Not just video conversion, almost all process that need lot of cpu can fail if the resource is not available.

Say as if you have 5 websites on a dedicated basic server with 50 people online at each site and try to upload, will it stop the encoding process due to too much resources being used else where?
It all depends on server load, how many people or web site you host do not matter.

And how do people find it on shared hosting packages having problems?
If you are asking about "Create Thumbnail" problem, i do not say it is because server load.

From my experience, this is due to ffmpeg installation (you may need reinstall ffmpeg-php too).

You can upload the video to http://video.bizhat.com and see if Thumbnail creation works, you are using the same code, so if Thumbnail not dot work on your server, problem is with your requirement installation or server.