Simple answer is no, and that also applies for other 3 phase lathes w/o a factory VFD install. There is a fundamental difference in that the native machine switches the motor high voltage motor connections, and typically the relays/contactors, controls work off of 24 VAC, or 120 VAC for larger lathes. If you connect the VFD run inputs directly to the spindle switches you bypass all the interlocks and safety controls.
If you want to retain the safety features and have the lathe work pretty much as if it was connected to 3 phase directly, then I previously outlined a fairly simple conversion which uses the contactors to switch the VFD low voltage control inputs. Not ideal, but as long as the contactors are new, the contact resistance/function should be acceptable. The basic conversion outlined takes maybe 1-2 hours to do and is very simple. You will spend a lot more time on building the VFD enclosure and outfitting it to a level you want. This information has been also previously posted. WIth a VFD, you have the added benefit of speed control and quicker braking. On a lathe, it is highly advisable to use an external braking resistor to get quicker braking times. I would also get a decent VFD, the WJ200-015SF that Matt sells and the parameters are included in the posting below. More recently I have also been using Yaskawa VFDs, but more complex and costly. The stock motor is decent enough and most individuals use a 20-90Hz speed range in sensorless vector control. This decreases the need to switch belts if used in the lower speed setting, or an alternative is to flip the motor pulley so the larger motor pulley goes to the larger headstock pulley, you will need a longer belt. This along with a 90Hz top motor speed will give you ~ the same top end spindle speed of 1800 RPM and no belt changes for low to high (this applies to the 1236GT/1340GT).
If you can swing the 1340GT, I think you will really enjoy it with the added VFD capabilities.
https://www.hobby-machinist.com/thr...l-board-and-switches.49022/page-2#post-564068