Yes, you can fill growlers. If filling from a tap, you can get a growler filler attachment that will fill the growler from the bottom, minimizing foam. Cap on foam, keep cold, and you should be good for days.
Two kegs in a fridge? If that was all I could get in there, I'd sure have two taps.
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Sounds like you're starting from scratch, w/ a budget of $600. I don't know if you are set on a refrigerator as your form factor, but if not, consider a small freezer converted into a "keezer." Tons of threads here on how to make one, it's not that hard. Mine has a removable collar that, if I were to do it again, I'd do it exactly the same way.
A keezer will allow you to have more kegs in there, which will allow for a pipeline, as well as a place to cold condition. At a $600 budget, you can get a small freezer for under $200, add an Inkbird controller for $40. Then you can add 2 good faucets like Perlick 650SS flow-control for about...$85 per faucet including shanks and tailpieces. That's top of the line stuff. So now you're up to maybe $400. Add a CO2 cylinder for $70, a regulator for $50, and you're under $600 with a very nice setup.
You'll have incidental expenses to create a collar on the keezer, maybe $30 or so, and you'd have a keezer w/ two faucets, expandable as you can afford, and room for 5-7 kegs inside depending on your needs and wants.
As soon as you start kegging, you *will* want more capacity. Heck, I can get 6 kegs in my small keezer and I wish I had room for a couple more. But a small 7 cubic foot freezer is a great place to start.
Here's a pic of mine. I painted it with chalkboard paint partly to cover up dings and dents in what was a used freezer. It shows 3 taps here (all Perlick 650SS flow control), I've since added a 4th tap, and actually have a 5th one waiting for installation. The nice thing with this is you can expand it as you have need and funding to do it.
Mine's fairly basic, there are some real works of art out there, but it does one thing extremely well: it serves me my homebrew on tap, whenever I want it.
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The newer version; you can see one advantage of painting it:
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