Hmmm....
Roman roads were ~4.2m wide and often more than 1m thick/deep. so ~4m^2 area.
the cross section of a Channel causeway 30m high would be 30*(30+4)m in area assuming a 45 degree slope. or ~1000m^2 area.
So.... Every length of causeway would take as much work as some 250 lengths of Roman Road. A 20 mile causeway would be like 5000 miles of road - and totally useless until the whole thing was done.
All order of magnitude/back of envelope calculations.
So.....
Would it be physically possible for the Romans to do this? Yes.
Would it be politically or economically possible? Nope. No way. No how.