Presuming that a deal is negotiated between the UK and the EU, there would most likely have to be a vote in the European Parliament to confirm it. Given that UK MPs would continue to serve in their function until March 2019, would they be able to cast their vote on said deal?
Yes. To expand on armatita's comment, from the same source:
The European Parliament will be important in determining the final withdrawal agreement. Whilst it has no formal role within the Brexit negotiation process, other than the right to receive regular information on its progress, the Council needs to obtain the European Parliament’s consent (Article 50 (2) TEU), voting by a simple majority of the votes cast, before it can conclude the withdrawal agreement.
Therefore, the European Parliament's right to withhold consent to the final agreement offers it political leverage to influence the agreement and effectively makes it a veto player.
Also, from the BBC:
Most of Wales' politicians in the European Parliament have raised doubts whether they will back the final Brexit deal.
Three of the four Welsh MEPs say a lot more work needs to be done on the final agreement between the UK and the EU.
It comes after the UK Government saw off a move which might have given MPs a decisive say.
Only Conservative MEP Kay Swinburne said she was "confident" the final deal would get a majority in Strasbourg.
Officials in London and Brussels hope to reach a deal before "Brexit day" on 29 March 2019.
Once an agreement is made, EU member states and the UK Parliament will be able to ratify it.
MEPs will then have the final vote - something which Welsh Labour MEP Derek Vaughan said should not be forgotten.
"It's not a done deal as far the parliament is concerned," he added.
"If it's a decent deal, if the UK government is saying we should stay in the single market and in the customs union, then probably we will vote for that deal.
"But if it's a bad deal or no deal at all, I imagine that Labour MEPs would not accept that. In fact, I don't think the whole parliament would accept that." [...]
UKIP MEP Nathan Gill, said the party was "very unsure about exactly how we would vote in that final vote".
"Maybe it is better that we vote against it and go out with no deal and we've said that all along - no deal is better than a bad deal."
So from the latter I conclude that UK MEPs will vote on it as well. While that is not 100% stated in there, I haven't seen any source that say otherwise (that the UK MEP's don't get to vote on the final deal in the EU Parliament final vote.) It would be silly for the BBC to convey what the various UK MEPs say about their position in the final vote if they don't actually get to vote (assuming there's something to vote on, i.e. an agreement is made and ratified by the EU member states [including UK] before).
In theory it might be possible for some UK parties to chastise their MEPs, and perhaps with threat of that to keep them from voting, e.g. chatisement happened before:
Two rebel Conservative MEPs who voted to block moves towards trade talks between the UK and European Union have been stripped of the party whip. The South West England MEP Julie Girling and South East England MEP Richard Ashworth were suspended from the party after supporting a resolution in Strasbourg declaring that “sufficient progress” had not been made in the Brexit talks to move on to discussions on the future relationship between the UK and EU.
But I'm not aware of a mechanism (short of consensus among all British parties to e.g. walk out) to keep all their MEPs from voting on the final deal. Insofar there's no indication that's gonna happen. In fact, in the aformentioned non-binding vote, there already was a sharp divergence between British MEPs based on party affiliation:
Mr Ashworth, a former group leader, and Mrs Girling, a former Chief Whip, broke ranks with the 21 strong group of Conservative MEPs to back the resolution, tabled by Guy Verhofstadt.
They were joined by 18 of Labour's 20 Euro MEPs, the only Lib Dem, Plaid Cymru and Sinn Fein MEPs and one of the Green's two Brussels parliamentarians.
Predictably the British government also called for the Labour MEPs to be chastised,
Brexit Secretary David Davis has now written to Labour leader Jeremy Corbyn urging him to remove the whip from 18 Labour MEPs who also backed the European Parliament's controversial vote. He has also written to Lib Dem leader Vince Cable.
but I doubt that request was given any following, especially given that nearly all (18 of 20) Labour MEPs did that.
No. The European Parliament members from Britain will not cast their vote on the said deal, because as with a surprisingly large number of things affecting Europe, it's not actually decided by the European Parliament.
The post-Brexit trade deal is likely to be the most complex part of the negotiation because it needs the unanimous approval of more than 30 national and regional parliaments across Europe, some of whom may want to hold referendums.
The quote above is from a BBC Article earlier this year. Ultimately the national governments control the membership of the European Union and it will be the National Governments, not the European Parliament that eventually agree or reject the terms of Brexit.
While the supplied quote talks about trade deals, you'll notice that all the news articles about Brexit negotiations refer to Theresa May, Angela Merkel, Emmanuel Macron and so on. None of whom are MEPs.