No. The Lisbon Treaty on the procedure for leaving the EU can be summarised as: "the state wishing to leave shall bend over and pick up the soap." - now, technically, it was a bit silly to sign up to that, but at the time nobody thought that the UK PM would be stupid enough to call a Brexit referendum and, even if they did, no PM would be gormless enough to lose such a referendum, and even if they lost the referendum no PM would be stupid enough to pretend that they were obliged to pay more than lip service to the result of an advisory referendum.
More specifically, the procedure under the treaty is:
(1) UK invokes Article 50 of the Lisbon Treaty saying it wants to leave. The PM has said she'll do that in March.
(2) Then the UK gets to negotiate a deal for leaving that, yes, has to be passed by the European Parliament "or, failing that, two years after the notification referred to in paragraph 2, unless the European Council, in agreement with the Member State concerned, unanimously decides to extend this period."
(3) At that point, the UK parliament may be given the option to approve the deal or reject it.
So, once Article 50 is invoked, the only way Brexit doesn't happen in March 2019 is if the European Council unanimously decides to extend the deadline. If that doesn't happen, and (predictably) the deal negotiations go to the wire then the only choice that the UK parliament will have in step (3) is "take the deal on offer or crash out of the EU with no agreement causing maximum chaos and confusion".
Oh, and note that the "deal" isn't necessarily this mythical trade deal that gives us access to the single market - according to some EU politicians we can't start talking about that until after we've actually left (and, in any case, negotiating such a deal in 2 years would be a new world record). No, this will just be things like who gets the cat, who gets the record collection and what happens to all the EU citizens living in the UK and all the UK citizens living in the EU (probably they'll get to go home on alternate Saturdays).