That is assuming you are using an inapporpriate shutter speed for the magnified focal length or increasing the ISO. .
Inappropriate? Do you mean, if conditions were such that one would use an unnecessarily fast shutter speed at base ISO
without the converter, then one could reduce shutter speed instead of increasing ISO when using a converter which requires a stopping down of F/stop?
I'd be wary about this approach, especially when using a 36mp camera. Maximum resolution is often dependent upon using a reasonably fast shutter speed, despite the benefits of VR. The higher the pixel count, the faster the shutter speed needs to be, except when using a tripod.
I shoot daytime sports with the AF-S Nikkor 70-200mm f/2.8 VR II and 1.4x TC-14EIII and find the results acceptable. And since I shoot a D810, I find a 1 stop increase in ISO not a problem, when I might need it, as I might have when I was shooting the D300.
Even with a so-called ISO-less camera, such as the D800 or D810, increasing ISO by one stop whilst doubling shutter speed, results in approximately a 1-stop reduction in DR and a 1-stop reduction in SNR at 18%. You can't get away from this, except by using Canon cameras where DR at low ISOs is approximately equally bad from ISO 100 to 400 and only about 1/2 a stop down at ISO 800.
You might well find the results acceptable when using a high quality zoom with teleconverter, such as the 70-200/F2.8. I would think the main advantage would be the ability to see the action more clearly because of the greater magnification. However, if you were to compare two shots of the same scene, with and without teleconverter, either using the same ISO but a faster shutter speed for the shot
without converter, or using the same shutter speed but a higher ISO for the shot
with converter, I doubt that you would find any meaningful benefit outside of pixel-peeping.
You should see a marginal increase in resolution when using the converter, if the lens is good. However, if the image without converter was shot at a lower ISO, it can be sharpened more, thus narrowing any resolution differences. If the image without converter was shot at the same ISO but using a shutter speed twice as fast, there will likely be some increase in resolution due to that faster shutter speed.