The problem with IDE CF cards is that these are typically marked as removable media. Some biosses will not boot from these and some software won't install on a removable drive.
Only in CF mode. Better cards support True IDE mode which means they behave as a IDE drive (fixed or removable). SanDisk (i.e Extreme), Transcend and Apacer have several cards that support True IDE mode in fixed and removable configuration, but usually only for the industrial variants, not the consumer cards.
Also, many of the cheap Chinese CF-to-IDE adapters don't put the card in True IDE mode, which is if I remember right by grounding a specific pin. Also, they don't connect the UDMA-relevant DMAACK/REQ signal pins. Nothing that can't be fixed with a soldering iron and a bit of wire.
I have used exactly the same mSata to PATA adapter in my Tektronix TLA715 because of these problems.
Never had an TLA but I've replaced IDE hard drives in a lot of similar systems (486 and up), with the right cards and a good adapter no problem.
Still I agree that the motherboard and CPU are rather poor choices. BTW UDMA is disabled in the VA-503A BIOS by default and probably for a good reason.
Probably. Which means you'd be using MWDMA which limits the board to 16MB/s (I guess a lot less with that chipset), which puts it easily into territory even an older/slower CF card could handle.