Its not bad at all, I do it all the time, of course its with Black Sunshine and she does not miss many meal (58 lbs!!).....
Seriously though, a 17-19 lb 338 am is not that bad to shoot without the brake. Not something you would want to do all the time but if your shooting from a standing position its not all that bad.
Figuring recoil energy is great, but remember that momentum plays a big roll in what you feel. The recoil energy is not that great but when you start a nearly 20 lb rifle in motion like that, you have to stop it with something and thats your shoulder, hopefully or your forhead will help in the effort.
The recoil is not a severe slap like you would expect from a lighter weight rifle, more of a heavy push but again, that heavy rifle put in motion will move you alot more then a light rifle.
My near 60 lb baby will slide 6-7" back on the bags when I shoot her and thats with my shoulder solidly against her. Its a slow push and you hardly notice it but after you shoot you realize your 1/2 foot farther away from the target then when you started!!!
The 375 Allen Magnum is a bit different beast, recoil on that one will do a better job at getting your attention. When I was going some testing on my big painkiller I pulled the brake off my 16 lb 375 AM without scope and touched a 350 gr SMK off at nearly 3400 fps. That was not nice.
A funny story on this same subject. A couple years ago I had just finished up putting together my first 510 Allen Magnum test rifle. My good friend Richard Graves came down one weekend along with another friend of ours and we played with her along with the 338 Kahn and Black Sunshine.
We were developing loads for the 510 AM and got the 835 gr Wildcat ULD RBBT loaded up to just shy of 2900 fps. After we got to that point we figured things were plenty hot enough and did not increase the load anymore.
We were sitting there just chewing the fat and Richard asked what I though the recoil would feel like without the brake. I looked at him, knowing Richard pretty well and knowing he is always up to a good challange, I said, don't know but I would give the man $20 to hear what it felt like.
After 5-10 minutes of trying to talk ourselves into it and also out of it it never happened but I am sure that nothing good would have come from that. It was in a 30 lb rifle but even at that, at well over 15,500 ft/lbs of energy, it was probably a good thing we finally decided it was not worth it.
I still think to this day if given the chance again, Richard would pull the trigger. Me personally, have no desire!!! LOL
You could shoot your rifle easily off hand and it would push you hard but it would not be overly uncomfortable. That said, line up solidly behind it off a bench and it will feel much different. Yes, the recoil is only about that of a stiff loaded 375 H&H but imagine an H&H that will push you back 7-8" when fired off the bench, totally different feeling.