Sure.
As long as you are aware that 99% of the recordings in existence were recorded and mixed with a mixing board. A lot of them sound pretty good for being "degraded".
I use a mixing board for monitoring, setting up as many as six individual stereo cue mixes, and general routing of various pieces of gear that make noise. (I don't use the preamps, however.) The convenience and ergonomics of working this way far exceed any concerns I have about some microscopic degradation that may be occuring, since similar degradation is occuring at the microphone, the mic preamp, the compresser, the A/D converter, the internal software calculations, the D/A converter, the power amp, and the speakers. To say nothing of the cable... there are some people who might tell me i should also be spending $100 per foot for designer cable or else i'm "degrading" my signal.
If working through a mixing board was good enough for all of the great engineers of the past, I'll take my chances on that particular issue not being the crucial factor in whether I can make a great recording or not.
While working in my studio may or may not be a degrading experience for my clients, I don't think their music has particularly suffered by having a mixing board involved in the process.
Yes, you should focus on gradually upgrading the weakest links in your system. Crappy gear that noticeably distorts your sound is clearly unacceptable. But the search for the perfect signal path is a quixotic goal - therein lies the path to insanity!
Until we can bypass mics, preamps, compressers, eq's, reverbs, converters, sampling and bit rates, and virtually anything electronic, i'm not going to single out the mixing board as the main culprit standing in the way of me and audio purity.