I don't doubt it. But I'll deal with the burn while the bear runs away.
Bears don't always notice a bullet. Not much different than a soldier that runs to a bunker, only to notice he was hit as he ran there. But the bear spray hits them hard with a nose that big.
The bear spray is also nice because you can go straight to it without a moments hesitation.
-Is it a bluff charge? Black bears bluff ALL the time. I've been bluffed 3 times already. I'm glad I didn't shoot 3 harmless picnic basket bears.
-Is it safe to shoot? Kids in the back ground?
-Am I going to jail for having a pistol here, and/or shooting it?
None of that hesitation with spray.
IF the bear gets a full dose in the face, and you only get a little blowback, that's great, as long as you can recover on your short walk back to you car and as long as the bear doesn't decide to charge you a second time. But IF you miss the bear with the spray, AND you get blowback, AND you're deep in the backcountry, now you're dealing with a real problem, as you'll be incapacitated for the better part of an hour and a predatory bear will not give up - it may retreat for a short time and then continue to stalk you. Furthermore, the MINIMUM time recommended to employ spray at a dangerous bear is SIX SECONDS. You have to hold the spray on the bear for SIX SECONDS for it to be effective. At 25 feet away, a black bear can cover that distance in just about two seconds, a Grizz in about three bounds, and sometimes they turn away and then charge again - if they think their bluff is ineffective, they may attack.
As I mentioned previously, if you're in the front or sidecountry, bear spray is sufficient - bears habituated to people are always going after your food, not you. I've treed or spooked bear that I didn't know were there until they started scrambling up the tree and chuffing, or running away - no need to shoot them with anything, but it does give you a good boost of adrenaline on a mountain bike or long hike. Picnic basket bears are not the issue, unless you are carrying your picnic in your backpack as the bear is trying to get it, in which case he may think YOU are the picnic. At issue here is the backcountry, in areas where bear/human contact is rare by default, but where the outcome of that contact can be dire. In those areas, families should always travel with small children between adults or immediately in front and close enough to touch, so you can move them behind you quickly. A bear will probably not notice a 9mm - but I guarantee you it WILL notice a .454 anywhere in its body. The 9th Circuit Court of Appeals just ruled that open carry is legal EVERYWHERE in the US, so you will not go to jail for open-carrying a firearm in public in the US. And you have to be alive to go to jail, so there's that. In other areas like Canada, you do need a license to carry, but it's not unobtainable.
You can go straight to a firearm without a moment's hesitation as well, and there's nothing wrong with putting a round in the dirt at the bear's feet - and knowing bear behavior is a must. Predatory bear behavior is very, very different from food guarding or protecting young.