From my unscientific tests... it seems that OOF blur is always more with the TC since you need to stand further back.
Also I am not 100% sure you can use standard DoF calculators for TC calculations (Maybe I am wrong again).
Then you need to do some scientific tests.

FWIW, standing further back makes your DoF deeper, meaning
less OOF blur, all else being equal.
Yes, the standard DoF calculators work just fine with a TC. For a 2x TC, just double the focal length and set the f/numebr two stops narrower, and you'll get the correct DoF calculation
This is not scientific but I came across this... why is Kenko claiming the DoF will be lower pls. see their description.
Yes, you can get shallower DoF with a TC - but
not for the same framing. What Kenko means is that you get 1/2 the DoF assuming you don't change the distance to the subject. Compared to 135/2, at the same distance 270/4 gives half the DoF...but frames a much smaller area.
For the most Part adding a 1.4x TC does add a stop of light, but no one has been able to convince me that the aperture (which determines DoF) magically closes down by adding a TC. Ye sthe system overall will lose a stop of light and "act" like a f/2.8 so that the camera can compensate for lower light transmitted, but the Aperture will stay wide open.
Ok, I think I see the confusion here...
What do you mean by 'aperture'? Of course the
physical aperture doesn't 'magically close down' - the iris diaphragm (the hole surrounded by aperture blades) doesn't get any narrower by attaching a teleconverter. But the
f/number is NOT the same as the physical aperture. The reason there's a slash or a colon in the f/number is because it's a
ratio of focal length to physical aperture diameter (both in mm, so the f/number has no units). A TC doesn't change the physical aperture, but it
does double the focal length (and cannot make the physical iris diaphragm larger, obviously), and that changes the f/number. I think this is the point causing the confusion here - the physical aperture doesn't change, but the f/number (which many people use synonomously with aperture)
does change when you add a TC.
Break out your calculator. A 135mm f/2 lens has an iris diaphragm diamater of 67.5mm (135 ÷ 2). Put a 1.4x TC on it, it's now a 189mm lens, and the iris diaphragm diamater remains 67.5mm. 189mm ÷ 67.5mm = 2.8. Put a 2x TC on it instead, it's now a 270mm lens, and the iris diaphragm diamater remains 67.5mm. 270mm ÷ 67.5mm = 4.
So, put a 1.4x TC on a 135mm f/2, and it's not 'acting like' a 189mm f/2.8 lens, it actually
becomes a 189mm f/2.8 lens, and has the OOF blur of a 189mm f/2.8 lens. Put a 2x TC on it and it
becomes a 270mm f/4 lens. The f/number has changed because the teleconverter increases the focal length.