I did a quick test. I did some of the adding of the units on paper, so if anyone spots an error say so, so I can go back and recalculate. This is with the second level of Returning Armada researched.
A Phase Gate costs 1,500 Credits, 200 Metal, and 300 Crystal on your homeworld. One all other worlds you have to develop Tactical Slots once to have enough, so the effective cost is 1950 Credits, 350 Metal, 375 Crystal.
The first group of ships that came to my homeworld (3 Enforcers, 1 Sentinel, 1 Assailant) had a worth of 3,065 Credits, 630 Metal, and 460 Crystal if I were to build these ships myself. Double the Credits cost, three times the Metal cost, and almost twice the Crystal cost of the gate. Up to two more gates for the additional cost could be supported at this world.
The next group came to my Asteroid (1 Transporter, 3 Assailants, 1 Sentinel, 1 Enforcer). Their total cost to build would have been 2,715 Credits, 505 Metal, and 370 Crystal. This batch paid for development and just 5 Crystal shy of paying for the gate too (the 800 or so credits though could easily be converted into 200 or so Crystal and make it up that way, if you wanted). One more gate, for the additional cost, could be supported at this world.
Next was my Ice world (2 Enforcers, 1 Transporter, 1 Assailant). The cost to build this group would have been 2,140 Credits, 485 Metal, and 360 Crystal. The Credits and Metal could cover the development cost, but Crystal was 15 shy and there wasn't a ton of Credits. You would have to sell off 100 of the Metal, and then buy 100 Crystal to even things out. Two more gates for the additional cost could be supported here.
I had one more planet, so just did a gate there for one more sample (4 Transporters). Their worth was 1,960 Credits, 440 Metal, and 380 Crystal, enough to pay directly for the game and the development. Two more gates could be supported at this world as well, for the additional cost.
This gave an average of 2,470 Credits, 430 Metal, and 392 Crystal worth of ships per gate per wave (1,235 Credits, 215 Metal and 196 Crystal if you just scuttled the wave).
All of the battle groups summoned though would have paid for themselves, either directly, or by selling and buying from the market, and arrived around 3 minutes after the gate's completion (an additional 5 minutes has to be tacked on for each additional wave). If you only wanted to scuttle, it would take roughly twice as long (so around 7 or 8 minutes for the next batch of ships to arrive).
The total teching to Dark Armada costs a pretty penny, 8,200 Credits, 1,550 Metal, and 2,425 Crystal by my counter (this includes the Phase Tunneling, Advanced Tunneling, and both levels of Returning Armada). It would take these four gates by themselves their third wave (around 12 to 15 minutes after completion) to pay for the research. If you want to throw in the costs of the labs as well, you have to wait for another wave.
This is all going on the presumption that use only 4 gates. If these four worlds are fully developed (up to 11 gates that would be) and we use the average from the first run of each gate, each time the gates all let lose a wave, it would 27,000 credits, 4,730 Metal, and 4,317 Crystal worth of units if you actually built them.
If you scuttle them just for resources, that would still leave you enough to pay for all of the research, the labs needed to do the research, and some of the development and gates, depending on the condition of the market. Wait for the second wave and you're well in the black.
And there will be a new wave every 5 minutes. With each planet you take, more room for more gates.
It's expensive to tech to, sure. But an amazing source for ships and resources that is literally unending. If you only do it with a few gates it takes a little while to justify it's cost, but once you start piling on the gates, it gets pretty crazy.
I know this all number crunching and hypothetical you could probably adjust the averages by a good 25% up or down (maybe more 4 samples seemed like a decent sample that wouldn't take too long, but 10 or 20 might narrow it down more). But I think it still helps explain why in practice Returning Armada is as good as it is.
And this reply shows how subjective the word "quick" can be, I guess.