Yes, the President can certainly veto such a law. Per the US Constitution (emphasis added):
Every bill which shall have passed the House of Representatives and the Senate, shall, before it become a law, be presented to the President of the United States; if he approve he shall sign it, but if not he shall return it, with his objections to that House in which it shall have originated, who shall enter the objections at large on their journal, and proceed to reconsider it.
This can have a very real effect: legislators are under no obligation to vote the same way on a veto override as on the original bill. The reason the President needs to supply written objections in the first place is that it lets legislators reconsider, see if they're swayed, or see if they think this is a matter where a Congressional majority needs to be respected even if they disagree (they can change their mind in either direction). They can also get a sense of public reaction. And because the threshold for this is "present and voting," it's possible that just more legislators show up.
Even if legislators won't be swayed, it still matters for pocket vetoes. That's where the President neither signs the bill nor returns it within 10 days; normally this is equivalent to signing, but if Congress adjourns in the meantime, it means the bill does not become a law. Because "Congress adjourns" is a necessary part of a pocket veto, it's impossible to override the veto (you can't do it if you're not in session). And even when this doesn't apply either, it matters for politics.
Example of a futile veto: Public Law 100-4. Passed 406-8 in the House, 93-6 in the Senate. Vetoed; veto was overridden 401-26 in the House and 86-14 in the Senate (note that at least 7 Senators who voted for the bill voted not to override the veto).
Example of an effective veto: While technically there was a conference report agreed to by both houses, and it doesn't seem to have had a roll-call vote (my guess is it was agreed to by unanimous consent; side note: many, many laws don't have roll-calls to check on, because they're passed by voice vote or unanimous consent), H.R.10929 from the 95th Congress was passed in the House by a vote of 319-67 and in the Senate by 87-2. After President Carter vetoed it, the House voted on whether to override the veto. The motion to override was defeated 191-206: after the veto, they couldn't even get a simple majority to override the veto of the bill which had been passed by an overwhelming supermajority.
I mentioned it above, but the two-thirds threshold is "present and voting." As a general rule, any time you see a fraction of something needed for a vote to succeed in a deliberative assembly, then unless it specifies some other denominator, it's talking about the fraction of members present and voting. Relevant CRS report on override procedure.