A base in Sudan gives Turkey the option to either protect or interfere with Red Sea shipping lanes; and as a staging base to reach their bases in Somalia and Qatar (noted in the 10th paragraph).
Egypt and Saudi Arabia oppose the Turkish base (from the first Strategypage link). Since the Saudis already bankrolled Egypt's purchase of two French Mistral helicopter carriers that France denied Russia in the wake of Russia's invasion of Crimea, those two probably figure they have the Arab forces needed for any operation in the Red Sea and don't need the Turks mucking around there.
A mobile base that Turkey will equip will be able to move between these bases to support them and project power beyond them to extend Turkish influence.
One possibility that Turkey may have in mind is making themselves useful to China by protecting the sea portion of China's One Belt One Road (aka New Silk Road) project heading to Europe to expand trade.
Turkey needs a patron until (in their mind) they are a fully capable (nuclear-armed?) regional power. Islamist ideology may make America (and NATO) unsuited to that role for Erdogan; and Russia is a long-time enemy of Turkey that is no more than a fleeting ally for dealing with immediate problems of a multi-war on Turkey's southern border.
Does Turkey see China as that patron to balance America and Russia? And if Turkey builds this security string of pearls network, will China come?
Turkey isn't going to rebuild their Ottoman Empire. Arabs don't have fond memories of Turkish rule.
But the Turks could be trying to extend their influence in much the same way that France has extended influence in former colonial holdings in west Africa.
Just as France relies on America to support their efforts when the going gets rough (and this isn't an attempt to insult France who I am glad makes the effort; it is a statement on capabilities) the Turks will find that they need at least American sufferance to operate this quasi empire.
Heck, if Egypt blocked the Suez Canal, the Turks are cut off from their new far-flung outposts.
So the question asked about whether Trump's anti-Iran strategy in Syria can survive Turkey's anti-Kurd operation in Syria is "yes." While we don't like what Turkey is doing, as long as it is largely restricted to west of the Euphrates River and doesn't have too many pictures of dead toddlers, America will grit our teeth and hope the Turkish operation ends soon.
The real question is whether Turkey's quasi empire strategy can survive American opposition if Turkey completely breaks with America (which I don't think makes sense for Turkey unless they have serious imperial delusions that include making Egypt their vassal state). I guess that is where China could come in.
Sure, we want to keep Turkey as an ally rather than drive them away. But that question isn't all on America. Turkey gets a vote on this, too, and they need to act like they want to keep America as an ally. Are they acting that way?
If alliance with America is what they ultimately want (and "they" is a unitary shorthand for Turkey, even though they surely have a variety of opinions within Turkey as to the value of America as an ally). I just don't know. But they are pulling away from both Europe and America.
So America should try to keep Turkey as an ally. My contrast of having Pakistan as an imperfect ally rather than an imperfect enemy applies here, too.
Oh, and I'll say again that I'd withdraw our nuclear bombs from Turkish soil. Turkey is still an ally. And could be a better one post-Erdogan. But they aren't that good of an ally lately.
As a process note, this post started as a data dump item of a couple sentences about the Sudan base, but it got promoted since I figured I had more to say about it as more news flowed by (yeah, lucky you, I know) and the China angle occurred to me.
UPDATE: Turkey is leveraging the Saudi-Qatar dispute to plan for air, naval, and ground forces in their Qatar base.
