I doubt it, there's no technical reason to limit the speed so slow. Also Good luck finding a 110mph ship that can deal with Atlantic swell. Hydrodynamics are still part of the laws of physics.
If it went from the West Coast of Ireland to Newfoundland at 110 Mph continuously, around 17 hours 30 mins, Assuming 186 Mph on solid ground, 1:30 across Newfoundland, 40 Mins in 110 Mph tunnels to Nova Scotia, just under 2 hours across Nova Scotia at 186, 1:25 to near Boston, 45 mins to Boston South via the Airport then 4 hours on Acela Tracks to NYC, an additional 3 hours to Washington for a grand total of around 1 day 5 hours to NYC, 1 day 8 hours to Washington assuming 2 hours for London - The West Coast of Ireland
If you went with 110mph (170km/h) you would have no business case for building the tunnel. The only solution to make it competitive with airlines is to use hyperloop technologies or Maglev trains inside a vacuum tunnel so you could remove air resistance and friction and allow the train to reach competitive speeds. But then that brings another issue regarding spacing between the tunnel vehicles in case of an emergency stop. At 600mph/1000kmh you would need to space them very far apart. If you went with something such as 5000mph/8000kmh you would likely only have one service per hour in each direction to account for the 18 minutes of acceleration, 18 minutes at speed, and 18 minutes of deceleration. For an international journey 1tph isn't too bad, but it's not very flexible either in that you can't simply add more services per hour if need be without potentially slowing travel times.
Well, the Eurostar trains through either the tunnels on HS1 or the Channel Tunnel are not doing the 186mph that everybody expects, certainly was not when I travelled from London Waterloo International to Brussels in the early 2000's. It was doing no more than 120 - 130mph if that speed. So on that basis, the journey to the USA, would take longer than the flight to the US.
This means that as well as building the tunnel to the US, you would have to build a complete new infrastructure for trains both in the US and here in the UK. The only trains that could compete with the planes, would be something like the Japanese fast monorail service which can do over 300mph.
Thing is though, would people feel happy enough being in a tunnel for several hours? Many people that I have travelled through the channel tunnel are glad when they come out of it and that is just 30 minutes, which is why i think it is a non starter.
With regards to 110mph ship, there is many fast ferries, that can do up to 50mph. Yes, many depend on the weather to be able to do that sort of speed across the channel to France and you also have the issue of propulsion where using diesel engines gives off fumes. However, many of the newer fast ferries are hybrid with being battery/diesel powered. The likes of Incat and Austal who build fast ferries, are working on ships that are not only fast, but friendly to the environment. An example is the Austal Volta Auto Express electric powered passenger ferry: