It is possible. Is it a good idea? That's for you to decide, IMO.
I have a 230v extension cord I use for my plasma cutter, and it has two boxes on the end of it - one with a NEMA 6-50 for the plasma cutter, and then another box with a 120v outlet. Is it to code? No. Is it safe? I mean the wiring in the cord itself won't burn, since it's all 8 gauge, but a 115v device that shorts might melt the outlet since it'll be able to push far more than 20 amps without tripping the breaker.
Main reason I made the cord is because 90% of the time if I have the plasma cutter out somewhere where I need it on a cord, I also need other equipment like my grinders and or my 115v MIG. The other "nice" thing is that most of the 115v outlets on my house are on 15 amp circuits which the MIG happily trips. The welder has its own internal 20 amp circuit breaker.
You could make it inherently safe by putting a 20 amp panel-mount circuit breaker inside the box with the 115v outlet. That eliminates the risk of overloading the 115v outlet.
I'm in no way advocating of making the "dual" 115/230v cord, but I have one, and use it regularly without issue as I know enough to not try and overload the outlet. I'm sure a lot of us here have a "double-male" 230v cord for our emergency generators, and those certainly aren't "safe" or "to code" either.