That depends very much on the specific machine, there are a lot of reel to reels that were never going to be the “gold standard” even straight from the factory (and the MX5050, which is the best I’ve ever personally owned, is one of those - it was a solid, workhorse professional machine for broadcast but it’s hardly a mastering deck), and if you’re using it as a creative effect rather than trying to get the most pristine master, those lower end machines can actually be a better (and more affordable) choice. I mentioned the Akai M8 specifically because I have experience with it and know that it’s still relatively affordable, but there are other options around. Some of the Pioneer-Technics quarter track machines are really nice and might fit in the OP’s budget as loing as they didn’t need too much service.
I don’t agree that mixing a 4 track cassette production to reel to reel will ahve “no audible effect” because I’ve been doing it off and on since the late 90s, and I know from experience that it definitely DOES have an audible effect*, especially at slower speeds that wouldn’t typically be used in a professional setting (I keep the Otari set up to run at 7.5ips and 3.25 ips rather than 7.5 and 15, because it colors the sound a lot more that way and I prefer especially hat it does to the low end over the more bright, hi-fi sound you get at higher speeds - plus the lower the speed the less important it is to keep it perfectly biased, and I’m lazy). But I do think it might not be the best choice for a cassette based workflow, which is why I mentioned the Tascam 122 series (used the wrong number in my previous post by accident, I’ll fix that as soon as I post this). I’ve been using an original 122 but by al accounts the 122 MkII is the one to get. They aren’t cheap but they’re still a lot cheaper than a 1/4" machine of comparable quality, and they fit really well with a portastudio, for the reasons I mentioned before (plus type II cassettes are vastly more cost effective than 1/4" reels). I’ll use 1/4" on a digital mix to give it some glue, and I’ll occasionally skip the computer altogether and record a direct to stereo mix on it, but when I pull out the old portastudio I’d personally rather use it with another cassette deck.
But it’s all really a matter of taste, and the emotional response to a particular piece of gear IS part of the creative process. Just the act of threading a tape and seeing the reels spinning WILL affect your work (HOW it will affect it is more subjective, of course) and even leaving the sound aside, for some people that can be enough to make it worth getting one.
Plus if you find a 3 head machine, stereo tape echo on a reel to reel sounds incredible.
*When I was a kid I was lucky enough to get one of those Pioneer-Technics decks for free and I would use it for final assembly - 1/4" was too expensive to use for everything, so I would mix down to cassette and then when I had an “album” worth of material I would dub the stereo mixdowns from cassette to 1/4" and edit the 14" tape by hand to get the final sequence. Then I’d dub that back to cassette and finally make copies of THAT cassette to give to riends an maybe ccasionally try to sell at a show, not that I played out much back then. A lot of generations across a few formats, and all of them had a very audible effect including the 1/4".
Or again, just download Airwindows ToTape because it sounds amazing (but don’t turn up the wow/flutter at all unless you’re using it to really mangle your sounds, or keeping it at the lowest possible setting - even a completely broken machine doesn’t ahve the kind of wow and flutter levels that Chris lets you add; I keep it on 0 almost all the time).
EDIT: responding to the post about the difficulty of maintaining a machine, that’s true if you’re looking to do pristine masters, but for these purposes it’s not so tough. Get it alighned once and then immediately make a “hosue tones” tape and stick it in a safe place, so in an emergency you can align it again without having to buy an expensive MRL calibration tape. In college I had a couple profs who came from the tape based studio days and all of them would do most of their alignments in the cheapest way possible. First, cover the head with grease pencil, run some leader through it, and then look at the shape of the bare patch where the pencil was worn away on the record head. If it wasn’t perfectly rectangular and centered over the head gap then adjust the head position acccordingly and try again - once you got the record head aligned to your liking you could align the repro heads with test tones. As long as the record and repro heads are well aligned with EACH OTHER, tapes recorded on that machine should play back well on that machine - since it’s unlikely anyone in this thread including me will ever need to exchange tapes with other tape based studios, it’s not so important that the machine is aligned to an accepted industry standard as long as it’s aligned to itself, because you’re jsut using it as an effect and then dumping to digital, not making a tape that’s going to be archived or anything. Spend 5 minutes cleaning it before you use it, maybe degauss a couple times a year, and you should be good for our purposes.
tl;dr - “unless you abuse it” is the key here, because abusing it is kind of the whole point of having any tape based machine in a home studio in 2019, and you can abuse reel to reel tape in really nice ways.