Of course they are

I don't know how long it will delay the testimony, but I imagine that's all it can do.  Trump is no longer the executive.   Also, there is no executive privilege claim in matters of crime or corruption.

...but hey, do what you want...you will anyway.

UPDATE 02/14/2023:

He's using the fact that he was president of the Senate on January 6 and should be excused on grounds of the Congressional "speech and debate" clause.  Bullshit.  The only speech he was required to make on January 6 was the one he did, in which he simply confirmed the electoral count.  

FURTHER UPDATE 02/14/2023:

Not just that, but his unseriousness as a truth seeker.  And value as a human being.

UPDATE 02/15/2023:

[Pence will] argue that because the vice president serves as president of the Senate, the subpoena would violate the protections afforded legislative officials under the Constitution’s “speech or debate” clause. It may be just the argument Pence needs — not to successfully avoid providing evidence against Donald Trump so much as to emulate his former boss’ success in running out the clock.

This ground is much less plowed than the executive privilege argument commentators have been expecting Pence to raise.

[...]

Moreover, federal courts in Washington have made quick work of the executive privilege arguments in recent cases involving former White House Counsel Pat Cipollone and his deputy, Patrick Philbin, and the Supreme Court has not reviewed their decisions. So an executive privilege argument might cause only a short delay in enforcement of the subpoena.

[...]

The contours of the speech or debate clause, which protects members of Congress from being questioned about what they say in the course of legislative proceedings, are underexplored and murky. That means the courts are likely to at least request briefing and argument and produce original constitutional analysis.

[...]

What is settled is that the speech or debate clause protects only “legislative speech” or “legislative acts.” [...] It would clearly prohibit, for example, arresting a legislator during a floor debate. On the other extreme, however, it clearly doesn’t prohibit prosecuting a legislator who takes a bribe or otherwise engages in criminal activity.

It’s hard to imagine a less “legislative” and more “executive” function of the vice president than the one-on-one conversations between Pence and Trump that are the linchpin of what the special counsel is seeking. The vice president may wear two constitutional hats, but that doesn’t mean he can put them on simultaneously. And for the purposes of the case Smith is developing, Pence was firmly in his executive branch role.p

[...]

[Another] problem here for Pence [...] is that he is no longer a legislative official. The subpoena was served on him as a private citizen.

Bottom line: Pence’s gambit should fail, but it probably won’t do so as quickly as a straight executive privilege argument. That means it could prolong the case into the heart of the 2024 presidential campaign. In that event, Smith might be forced into a choice between forgoing Pence’s testimony or conducting the first-ever prosecution of a former president in the middle of a campaign in which he is the front-runner for a major party’s nomination.

[...]

The former vice president could likely provide devastating evidence against his former boss that could help secure federal charges against Trump and make his own path to the presidency more feasible. But with former U.N. Ambassador Nikki Haley jumping into the race Tuesday and other Republicans poised to follow suit, Pence appears to have concluded that he still needs to tow Trump’s barge lest he completely lose the 32% or so of the electorate that is inexhaustibly faithful to Trump.

[...]

As ever, Trump and his former cohorts are taking the Justice Department, the courts and the country into new and scarcely ponderable territory — and giving rise to seemingly endless delays in holding the former president to account.

  LA Times

I've only read that Trump is expected to join the fight on executive privilege claims, but not that he has actually done so.

UPDATE :02/15/2023 01:28 pm:

He still has a Secret Service detail, so it's not that he's afraid for his personal safety.  He doesn't want to turn off ALL MAGA voters.  But, honestly, does he truly think he can get any of them anyway?  They were ready to hang him.