The short answer is no. Administering gas-only anesthetics is difficult. There are stages to the body reaching that peaceful looking anesthetic plane, and one of them is the “excitement stage.” That’s the one where the patient starts leaping around and gasping. It’s why it’s been deemed, at the very least, unusual. I use this method occasionally with cats when they’re feral or otherwise untouchable and giving them an IM shot of another anesthetic isn’t possible for some reason. It’s not a fun procedure, and no amount of tying the patient down suppresses the alarming state.
Pentobarbital.
The manufacturer of pentobarbital will expressly NOT sell it to anyone for the purposes of executions. So it cannot be gotten for executions unless by illegal means. Since the paper trail for the purchase of execution drugs has to be pristine, pentobarbital cannot be on the list of what can be used.
There’s an easily followed paper trail on controlled drugs, from manufacture, to distributor, to doctor. So anyone trying to fudge it along the way will be caught. Pentobarbital is sold for veterinary use only, so for a regular MD to get hold of it would raise eyebrows immediately and would swiftly lose their license.
When euthanizing people’s pets, we use propofol as a preliminary anesthetic. This is the same drug used for people and pets for surgery, to get them sedated enough to intubate before starting gas anesthesia. It’s not a controlled substance, and can be had by all medical doctors, but I don’t know about the manufacturer’s stance on using it for executions. It’s also extremely short acting, so it’s likely not appropriate for use if the second fatal drug isn’t fast acting enough. Though, many may remember it’s the drug that killed Michael Jackson - administering too much too fast can cause respiratory paralysis. Probably arguably not a good way to go and is probably considered cruel and unusual.