We typically have a question every month or so exactly like this. The reason has a very technical answer, but I will try to put it in laymen terms as best as possible.
There is a "bargain basement" company that claims its a cinch to add a spool gun to their TIG because the fittings match up. Maybe they can, who knows? But I doubt it.
There are generally two types of power sources: Constant Current (CC) and Constant Voltage (CV). Constant Current is required for TIG and STICK processes. The current remains fairly constant but the voltage varies because the actual voltage is controlled by the arc length. As the arc gets shorter, the volts drop and the arc tends to go out and even stick (if it gets too close to the base metal) because there is not enough total wattage to sustain a welding arc.
The Constant Voltage machine is typically your MIG or Flux core processes. The voltage remains at a steady level as the arc is constantly shorted to the workpiece and the metal is transferred. The current varies with the length of stickout of the wire. One reason you'll seldom see a current reading on a stand alone mig is that the wire speed IS the amperage. Though its not an amp equivalent, the speed with which the wire is fed determines actual amperage output.
Now there are subset terms within the CC and CV categories such as droopers and constant potential that describe nuances of these two basic categories. But I won't discuss that here...some even gets beyond my reach. However, there are a couple of things that will allow a wire feed unit to run on Constant Current. The wire feeder must be able to sense the voltage and compensate the wire speed for the increase or decrease in voltage. Many "suitcase" wire feeders that portable welding guys carry are this kind of wire feeder. However, most users tend to agree that the voltage sensing wire feed system is not ideal. It is a "get by" approach to welding MIG when nothing else is available as a power source. A lot of older "pipeline" welders were only able to provide CC voltage and thus the need for voltage sensing wire feeders as wire feed units became popular on the job site. Modern units now have taps that allow CV operation. But I digress...
Getting back to why a spool gun won't work on a typical TIG/STICK unit is that spool guns (at least the ones most people provide) are not voltage sensing and operate with a steady wire feed control. What typically happens if a spool gun is operated in CC is that the wire feed will appear to be very erratic, while its actually the arc is not being controlled and frequent burn back and start stopping occur with very little usable welding happening between.
Now the thing about inverters is that an inverter can be made to produce both CC and CV current relatively easily. The problem is that most tigs are not produced with both CC and CV capability, especially with the cheapest importers.
Our smallest I-MIG products, the I-MIG 160-200-205 are both CC and CV capable. They can be used for stick or scratch start tig (in a pinch). These inverters are very good at both MIG and STICK...one reason our price is not as cheap as some of the other "import" brands like HF which produce low duty cycle transformer machines. An advantage that the I MIGS have is that they have Arc Force control. The arc force control in MIG is also known as Slope or inductance (another whole lesson). Suffice it to say, that arc force's practical application is that it controls the welding arc qualities. It can make the unit with a soft buttery arc with a very liquid puddle, or a stiff, harsh arc that is very tight and defined with very little lateral wet in of the puddle. There is nothing wrong with either extreme, as each has its own applications. In stick mode, the arc force helps to boost amps as the arc is held short to keep the arc stable and the puddle hot.
Now back to the question if a MIG can have CC/CV then why not TIG? Well, space consideration is one. With advanced tig features, there is very little room left for a dedicated CV circuit. Also, tig is considered the preferred way of welding aluminum or any metal for that matter. This makes a spool gun as unnecessary as mammary glands on a male porcine animal. I have looked at these so called "spool gun" capable tigs and have seen nothing to indicate that they have a special CV setting. Just because a spool gun will hook up to a tig unit, does not mean that it should hook up to it.
Sure it is possible...but not probable to have a TIG/Spool gun combination. Spool guns are extremely expensive to operate, with lower quality welds than a tig. So why would someone jeopardize their weld quality by using a spool gun when a much better option is at their finger tips? Again, adding a spool gun is possible with the right technology, but does it really make that much sense?