What if the execution time for an alt coin script exceeds the block time? I don't know when and how often a script is executed, but it seems to me that there would be a problem if a single script (or a sum of all scripts in a block) exceeds the time it takes to be included in a block. 

Given that the trend in alt coins is to decrease the block time duration,  I think this could become an issue or race condition where the TX never gets included in a block. 

Considering that as the various alt coin block sizes grow ... Perhaps larger than 1mb, this risk would grow as well, given the higher quantity of transactions. 

So my question is: 


When are transaction scripts evaluated (or not )?


I heard that certain old TX scripts aren't validated during the initial sync to speed up the process, so perhaps there are other times that a TX isn't executed. (Perhaps it's an unknown script.)


What role does CPU load have on the network and the risk of a fork?


Perhaps only miners are only affected.... I'm unsure.


If the network running full nodes has capacity issues with either CPU or bandwidth could a fork occur?
You shouldn't need to worry about this ever happening.

There are no loop opcodes in scripts. Every script opcode can only be executed once, and the slowest opcode is probably ECDSA signature verification (because it involves EC_point_multiply). Even so, it only takes about 50~100μs on a single core of a modern CPU to process.

Let's assume a 1MB block (max size) contains 100% signature verification opcodes, that's 1 million signature verification and takes at most 100 seconds CPU time of a single core, this is still much lower than the block time. In practice each scriptSig is accompanied by at least 100 bytes of data (pubkey + ECDSA signature) so it probably takes less than 1 second of CPU time.