Well, this question has been asked here MANY times before, and answered just as many, but here's my experiences trying this.

I started with an AC 230A buzz box, and made my own bridge rectifier from some enormous diodes I found on eBay (500V, 500A rated, originally from some huge rectifier), bolted down to some copper bus bar I got at the scrap yard, and a 2x6 (as the insulator, first coated with dielectric varnish).
The DC output from this was a pleasant upgrade from AC for stick welding, but was wholly unsuitable for scratch start TIG.
I then added a high frequency box, which made TIG possible for me, but if your DC is clean enough, you may be able to scratch start with just a torch and gas.
The HF box was really neat, and quite affordable (also from eBay), and I had fun playing with it with stick electrodes (its a weird feeling to start a stick without any contact).
I also have a torch with a valve on the handle from this project.

The results were disappointing to -me-, but it all depends on your expectations, and what you plan on doing.
For me, it was a very fun and rewarding project that lead me on to buy a real TIG machine.  That valve on the torch now gets annoyingly uncomfortable, since my TIG machine has a gas solenoid valve built in, so its now unnecessary.

My biggest problem with the buzz-box TIG, was the inability to have amperage control.  This left craters at the end of every weld, and I always found it was either too cold, or I was struggling to keep up with the puddle.

Of course, with a dedicated TIG machine, you can also get squarewave output (night and day difference in the arc), automatic pre/postflow (less think about means less to mess up), lower amperage output (buzz boxes really don't perform well below 70A), HF or lift start, etc.

Since the current will be in the same range as you use for SMAW, don't expect it to be less likely to blow through thin sheet than stick.  But if you're welding 1/8" steel and up (limited by your torch's capacity), you will get cleaner results than stick (its nice having no spatter anywhere), any may just be happy with it.
Also, remember that GTAW has MANY MANY variables, so if your results are not good, it may or may not be because of the limitations of your machine.  Just bring your questions back here, and I'm sure someone will set you straight.

It will weld just fine as long as you add a flow meter to your list. However depending on what you intend on using it for will determine how much you like it. People have used this set-up in the field for years on everything from sheet metal to nuclear grade alloy piping but it lacks the ease of operation that a shop machine will give. A "dry rig" requires that the amperage be in a range that you work within because you don't have a reostat to adjust on the fly, you have to scratch start and set a travel speed and arc gap which coincides with whatever weld bead result you are trying to achieve. It will take more practice and time to learn the skills required to get results that are similar to purpose built TIG machines with their added functions. This is the set-up of choice for field welding as far as portability and durability.