No, it won't show up in OBD codes, TFI system is separate from computer, if it had failed outright it would set a no PIP code but that's not what you have
1995 and up computers had the spark timing system inside computer so could detect some of these issues, but never had the heat issue, so.........
Testing is to see if there is a wiring problem before replacing TFI module.
Another test is to heat up the engine so it doesn't start the first time like when cold.
Place a bag of ice next-to/on TFI module for a few minutes to cool it down, remove ice and try to start, if it starts up replace TFI module.
Test Coil the same way but NOT at the same time or you won't know which is failing when hot
Electrical systems get higher resistance when heated up, that's how your engine temp sensors work, TFI module or coil can get too high of a resistance when heated, so fail to provide spark or enough spark to start engine.
And corroded connectors will lower voltage to TFI and Coil when heated up, which is why you should test the wire first, sometimes just unplugging and plugging back in a connector can clean up the contacts enough.
90% of sensors replaced by DIYers were working fine, many just had dirty connectors which is why replacing it fixed the problem, connector got cleaned off.
But old sensor tests as OK??????, so if possible always test first, save yourself some money, $20 volt/ohm meter can save you hundreds of dollars
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