If a vote of confidence in Theresa May is triggered, it is likely that she will win it by a big enough margin to enhance her authority.
The Commons vote on the Brexit deal presently looks short of numbers, but this could change. MPs might prefer the deal on the table to no deal at all. They might decide that it delivers most of what the majority of voters wanted in the referendum. Some Tories will vote against, but some Labour MP’s will vote in favour. Once it becomes clear that a second referendum is not going to happen, and that remaining in the EU is not an option, MPs might vote to avoid a hard, no-deal Brexit.
If it is carried, then next March 29th the UK leaves the EU on those terms. If it is not carried the government has 21 days to come up with a new plan. This will likely be the existing plan with a few EU-agreed modifications on the border issue to now carry it through.
It is then highly probable that within the two-year transition period, a free trade deal with the EU will be signed, rendering unnecessary the arrangements on the Irish border that some have objected to in the proposed deal.
The UK will have left the Common Agricultural Policy and the Common Fisheries Policy. It will control its borders and its immigration policy. It will no longer pay billions into the EU every year. It will negotiate free trade deals outside the EU, and its citizens will enjoy visa-free travel within the EU.
It will have left the EU, as its citizens voted to do in 2016.