A thought just occurred to me, what if in this episode it wasn't the Odyssey that was lost but rather the Enterprise-D. How might that have changed things? Would all the crew have survived?
It's hard to imagine TPTB ever letting that happen. The easiest way of course would be for the Jem'hadar to simply not engage in their kamikaze attack at the end. The ship would survive but be heavily damaged, and the Dominion would have made it clear that they meant business without pushing it quite as far. If they did go that route, I hope they'd at least provide casualty figures at some point and mention how close the E-D came to being destroyed.
It's very unlikely for two reasons: TNG aired their finale May 23, 1994. The Jem Hadar aired June 12, 1994. The TNG cast had just wrapped up their television series and were looking forward first to the summer's break, then to making movies. Fans were pretty happy with how TNG wrapped up. The producers were not going to bring them back to be co-stars and blow up their ship. The fans would hate it and the actors would hate it. Second, the Federation and Starfleet are supposed to be big organizations. The Enterprise shouldn't be "the only ship in the area" every time something goes wrong.
I'm not sure, but I think that the OP's question presupposes that Generations would not happen, or that the TNG crew would be outfitted with a new Enterprise that would not be destroyed in the movie. The question would still have other problems, of course. The Odyssey was meant to represent the Enterprise in some manner, but I would have difficulty seeing Picard engaging in a "show the flag" mission. Although 1701-D had its might, he tended to use a conciliatory approach. I doubt that he would have been any more successful. I think the question that would get raised is what would happen when Picard realized the scope of the jem'hadar onslaught. Would he consider four people sufficient reason to risk the destruction of the ship and loss of crew? There were times that 1701-D faced destruction, but the stakes were obviously much bigger (Yesterday's Enterprise, All Good Things), but more often than not, trickery could be used to resolve the situation (as when Troi posed as a Romulan agent). One incident might offer some insight: how Riker reacted to Jellico's refusal to help rescue Picard suggest that the crew might be willing to sacrifice strategic interests in favor of recovering officers.
Very much the line of thinking with the SG teams about not leaving anyone behind in the STARGATE shows.
Were the writers to insert the E-D here, the dramatic rationale for that would probably dictate major casualties among the key heroes. Otherwise, what would be the point? I could certainly see everybody dying, although some drama might in theory be wrung out of a single TNG cast member surviving. See below. On the practical level, if the writers did decide to slaughter the TNG characters to further the general Trek agenda, they would probably only be able to afford a couple of the leads for the DS9 season finale. Say, we might see Picard, Riker and either Worf or Data on the bridge, with dialogue excuses made for the others being aboard but offscreen (perhaps literally phoning in a few lines at best). Or then they might go the "unload nonessential personnel" route and have Crusher or Troi or even Guinan participate, left on DS9 (while half the audience would seethe at the insult of their favorite being declared nonessential) and then commenting on the deaths of all her colleagues at the conclusion. Heck, they could even use Wesley there for their take on the ultimate tear-jerker. This would reduce the number of characters visible aboard the ship, though. As for Picard acting differently from Keogh, I don't see the opening for that. There was only one real decision to be made, whether to enter the fight or to turn back. Once the fight got going, withdrawal was no longer a factor: indeed, it was at the decision to withdraw that Keogh sealed his fate. Timo Saloniemi
The Enterprise would have been destroyed. O'Brien would have been a bit sad. Enterprise-E would probably have been the exact ship but with a different crew. Worf wouldn't have joined the DS9 crew.
That may have worked. The producers wanted to destroy the Enterprise D during TNG season 7, so that there could be a new ship for the first movie, but the idea was ultimately rejected. You'd have to find out who it was exactly that wanted to destroy it in S7, and who was against it. Then look at who creative idea destroying the Odyssey was. You just may find a connection. Let's say it was Michael Piller, and he just really wanted to blow up that ship, so he said "Fine! I'll just blow one up on my new show. I dare anyone to try and stop me
I thought it was a mutual decision by all involved to destroy the Enterprise-D. They'd wanted to crash the saucer since the sixth season but couldn't afford it on a TV budget, and since the models or sets didn't look so great on film (according to those involved) they decided to kill two problems with one Bird of Prey.