In Europe all the major lines are already electrified, and because all the lines were built a long time ago (generally in the 19th century), the construction carbon emissions are divided between 150 years of transported passengers.
In any case, I think its fair to say over time trains win out over airplanes on emissions, but it isn't that cut and dry especially early on.
400k seats a day, or 150 million a year, for an average 10kg co2 per seat in construction costs over the first year.
456km London to Paris is is about 100kg co2 each way per seat.
So construction emissions isn’t even a dent in the first year.
I also doubt they make up a substantial part of the rail traffic, if we go about it that way we there's a whole bunch of vehicles with horrible CO2 emissions that only have gotten barely viable electric alternatives in the last handful of years, like excavators, bulldozers and all kinds of other construction/hauling/maintenance vehicles.
However, railway vehicles tend to last for decades, so it might take a long time for everything to be electric. The people buying them can both afford and have the expertise to purchase reliable, repairable equipment. It's then run on a perfectly smooth "road" without much rough handling.