wow...well I'm not sure exactly what type of tape machine we are talking about, but I'll just lay out some stuff and you can use the information as you wish:
Analog does have its sound, but alot of that also has to do with having a really good tape machine. If any tape machine, whether new or old is not properly calibrated or in poor condition, I don't see any benefits of running daw mixes through it. So I'm not sure if you're used to calibrating tape machines, but that's just part of the gig.
Which means you need to spend money on an MRL, for starters. That's how you're going to cal your tape machine. One of those can run you a few hundred dollars. Then you'd have to set operating levels (ex. +6 or +9 operating level?), keeping in mind the type of tape you have and do all this stuff to get the machine working the best it can. In fact, some people make a good living just calibrating tape machines all day.
Without that calibration and maintinence, your frequency range could be compromised, your dynamic range could be compromised, your phase could be compromised, which means it was better to stay inside the DAW anyway. You'd have to consider your tape speeds (15ips or 30ips) and the benefits to each, and that they even make the type of tape your looking for. Not all reels sound the same, nor do they perform the same.
Then you'd have to check the condition of the tape heads. Replacing those can get really expensive. On a studer 2inch tape machine, that can reach up to 13grand to get good heads.
Oh and demagging the machine also comes up. Usually a special tech does that. If you don't do that, you risk having bad high end response.
If it's a good tape machine, and you have knowledge of how to calibrate one flawlessly, then it can help you out a little more. Even then, it's the A/D conversion that kills you.
So it's give and take. If you're able to accept some loss of quality at the expense of passing mixes through a tape machine, then go for it.
On the plus side, tape does gel things better than a DAW could ever do alone. It smooths out your highs and rounds off your lows. I will gel things in the overall mix better. The 2nd and 3rd harmonic distortion will give a pleasing sound to the human ear. It makes a song sound like a song (in my opinion).
I guess the reason question is: If you're good at calibrating that machine, able to take on extra expenses for nessessary items, know exactly what type of tape you want (if they even make it anymore), know the general result to expect and are all around proficent with a tape machine, then maybe it's worth your while.
If you feel a little unsure about how to use one, I can't say that it will benefit you in any way. Of course, that's just my opinion. Not my money.