I'm not an electrician, though I have an electrical background.
As far as running "in line", a 220VAC breaker spans both 120VAC legs of an electrical panel, so theoretically, it shouldn't make a difference (as far as power draw is concerned) if you are running two seperate 240VAC breakers, or "pig tailing" two outlets off of one breaker AS LONG as the breaker is rated at a combined capacity of both tools that will be running at the same time.
Granted, you should keep in mind what your "overload" protection may be reduced in the event of a surplus current to either machine. Your VFD will likely have built in protection, so it shouldn't be as much of a concern, but I'm not sure about your welder.
For example, if you're running a 25 amp welder on a 30 amp circuit, you are protected (via the circuit breaker) if you have a 5+amp surplus to the welder. Now, if you add a 3hp motor in line with that circuit (draws about 8 or 9 amps?) you'll want to increase to at least a 40 amp breaker in order to be able to run both machines at once. This means that it will take 10 more amps of "over current" to trip your breaker and protect your welder, or 30 more amps if just the VFD is running.
This also assumes that your conductors (wires) are rated for the potential full loads you'll see on this circuit. How big is your welder? What size wire are you running to the welders and its outlet?
All this being said, (assuming the overall circuit is up to spec) this probably won't be a problem in standard practice, but it is something to keep in mind.
Remember, a circuit is built for the load, and a breaker for the circuit. When you start splitting loads (I.E., running multiple machines at once) you are forced to rely less on the protection of the breaker panel, and more on any built in protection of the machines themselves (fuses, thermistors, internal breakers, etc...)
Clear as mud?
Somebody please correct me if I'm wrong or stated something incorrectly.