Image copyright Getty Images Image caption President Trump's order will be read as proof that the US government is anti-Muslim

Yes, in a word.

There is no scientific way of accurately measuring how many people will be so incensed by President Trump's executive order on immigration from seven Muslim-majority countries that they feel compelled to carry out a violent act against a US or Western target. Perhaps dozens, perhaps none.

There is also no scientific way of measuring how many potential violent extremists have now been shut out of the US because of the order.

But one thing is clear: in the ever-shifting ideological battle to win hearts and minds, this is one-nil to the extremists of so-called Islamic State (IS).

Iran's Foreign Minister Javad Zarif, whose country is currently helping Iraqi forces drive out IS, said the US move would "be recorded in history as a great gift to extremists and their supporters".

He added that it "only serves to provide a fertile ground for more terrorist recruitment by deepening the ruptures and fault-lines which have been exploited by extremist demagogues".

In Indonesia, the world's most populous Muslim country, a foreign ministry spokesman said it deeply regretted the move "because we believe it would affect the global fight against terrorism… It is wrong to link radicalism and terrorism with one particular religion".

Even America's closest ally, Britain, has been critical. Foreign Secretary Boris Johnson tweeted that in his personal view the move "is divisive, discriminatory and wrong".

Behind the scenes, where the ideological battle against violent extremism is fought in internet chatrooms, over anti-terrorist hotlines, and with tip-offs from the public, one effect of the immigration order will be to, at least temporarily, inhibit co-operation between the US and the very countries whose help it needs in fighting Islamic extremism.

Iraq, whose forces have undergone an extensive retraining programme with help from US advisers, has been quick to retaliate by imposing similar restrictions on US visitors.

Image copyright AFP/Getty images Image caption Many Americans have joined protests to show their opposition to the divisive policy

At street level, anything that portrays the US government as being anti-Muslim - and that is exactly how this is going down in much of the Middle East - makes it harder to fight the narrative of IS and other extremists.

Largely obscured by the tumult and confusion over President Trump's Executive Order is one simple, compelling fact: the people whose actions bear the original blame for much of the mistrust and negative stereotyping of Muslims, on both sides of the Atlantic, are not the mainstream Muslim populations themselves.

It is the extremists from al-Qaeda, IS, al-Shabab and other affiliate groups who have waged violent jihad in the name of their common religion.

Through their actions, these extremists are looking to separate Muslims from non-Muslims and to create a gulf between them. They crave a return to a time when much of the inhabited world was divided into Dar al-Islam (lands inhabited and ruled by Muslims according to Sharia, Islamic law) and Dar al-Harb (literally "the House of War", meaning all the other lands).

Anything that helps polarise the world's populations further down this path of segregation and an "us and them" mentality is welcomed by the extremists.

When refugees surged out of Syria and headed west towards Europe instead of into the self-styled IS caliphate centred on Raqqa, IS's leadership was baffled and angry, viewing this as treachery.

The executive order on immigration now risks playing into their hands.

As IS finds itself ruling an ever-shrinking area of territory in the Middle East, it can be counted on to take maximum advantage of this latest development to recruit new followers and urge existing ones to carry out attacks.

Some of those may already be living inside the United States.