This is correct. Most add-in cards for drives, such as RAID controllers or M.2 adapters, are built around the BIOS design and as such won't allow you to boot from drives connected to it.
As for the original question, this is what BF1's load sequence looks like from a system perspective;
I joined just as a map was finishing, but actually got into the game just before it ended. The red line is when the loading starts, and the green line is when it ends. Despite running on a SATA-3 SSD that can push 500MB/s in sequential read speeds, the maximum load I saw from it was around 240MB/s during BF4 map loading. My HDD can push 150MB/s read speeds without a problem, but the access time on it means that large games aren't suitable for running from it.
The access speeds are the key for SSD's, so even buying a moderately sized SATA SSD would be a good upgrade. The 2GB/s speeds are only in benchmarks which tend to use one large continuous file, which once access is setup, doesn't need to be done again. With games, since they're lots of smaller files, access speeds are king. Further to this, every large multiplayer game does a lot of network sync either before or after load or both before and after. Install a game to an SSD, and you've still got to deal with this which becomes one of the bigger delays in getting into game.
With all that said, you won't be bottlenecked by setting it into a converter in real world usage. The only time you should expect to see some limits is if you're running benchmarks. PCIE 2.0 still offers 500MB/s per lane, so a 4x slot or adapter, which is likely what the add-in card runs on, will still offer 2GB/s maximum throughput. Trust me - you genuinely don't need even that much for a gaming rig.