Air travel may be a small part of total emissions but it's one of the few that's increasing, with some scientists saying that CO2 discharged directly into the upper atmosphere is more harmful than on the ground. It's also one of the few sources with no obvious technological route to bring it down - electric planes are mentioned but they look to be only suitable for short haul flights for which trains are already often a good alternative. So we may see measures such as higher rates of passenger duty on those shorter flights, or even aviation fuel taxes large enough to make a difference. Either would be politically very difficult and wouldn't dent the price advantage of flying by very much - though the figures are a bit better if compared with a flight plus hotel.
This may explain why there seems to be a bit of renewed interest in overnight trains, for example with OBB taking over routes formerly run by DB. I'd say the range is a bit further than you suggest, with up to 12hr (London-Berlin according to Rick) being possible for a sleeper but anything less than 8hr being too short for a good night's rest. It's complicated by most high-speed routes being closed at night, though HS1 would be working at the times London sleepers arrived and left.
The lower passenger density of a sleeper makes the passenger number issue slightly less bad, as the capacity of the train is about the same as that of a 737/A320 on an early morning flight. There are plenty of destinations about the right distance away having one such flight - in fact the opposite problem exists as the rail network wouldn't have enough capacity to replace all of them. The extra weight per passenger of a sleeper also reduces its environmental benefit.
Even if all this happened on the Continent I'd see the UK as being about the last place to benefit. Our general semi-detached state creates political risks for an operator. They would have to comply with Tunnel security procedures as mentioned, but also with Tunnel fire procedures which probably rule out standard European stock. If going beyond London there would also be the loading gauge issue, which makes quite a big difference to sleeper capacity.
Even if 'some scientists' claim that carbon dioxide released into the upper atmosphere has a greater effect on global warming that the same quantity released at ground level sometimes one has to accept that there is a cost to every activity done by man. Have you ever asked yourself why air travel is increasing? Could it be that it is filling a need/want/desire more effectively than an alternative?
The number of flights which could be avoided by an expansion of sleeper or other overnight trains, will not be great. Even if one could get from London to Berlin overnight in about 12 hours that still means that train would replace one flight at the most and the number of city pairs in Europe that could support such overnight services is limited. As you say, anything less than eight hours is too short and anything longer than 12 hours loses out to a night in one's own bed and then a flight. So one is looking at city pairs between 8 and a maximum of, say, 14 hours apart at night train speeds and which have a sufficiently large travel demand between them to consistently supply 150 to 200 people per night in each direction. Rome to Frankfurt-am-Main or Berlin might just be possible, Bordeaux to Warsaw won't and neither will Göteborg to Tallinn.
And this example brings us back to the UK. I say again, regardless of any other constraints, geography is against rail travel from the UK to the near continent because the ONLY crossing is in the south eastern corner. Any rail route has to go this way which will therefore involve significant dog-legs except for those cities for which the Tunnel is already on or near the shortest route. It is no accident that air travel per capita is highest for people living on islands.
Anyway, even if there is a marginal decrease in the growth of air travel in Europe such developments will have no effect whatsoever on carbon dioxide emissions in other parts of the world. I am in Germany at the moment and have just learnt from a TV programme that although Germany has very high levels of CO2 emissions compared to other countries in Europe (in spite of covering the country with wind turbines) resulting from the use of brown coal (lignite) for electricity generation total German emissions make up only 4% of the worldwide total.