ASB no, but extremely hard, yes. A long succession of enclosed sea to get to the nearest ocean, for one, meaning that contact with the colonies can only be kept depending on the goodwill of whoever controls Bosphorus, Dardanelles and Suez/Gibraltar.
However, here's a take (caution: highly concentrated handwavium):
- Napoleon delays his attack on Russia to 1813. Russia has additional time to mop the floor with the Ottomans in the Danubian principalities and forces a treaty whereby they are ousted from the area altogether, among other gains (Kars, maybe). However Alexander is quite aware that trouble with France is coming, doesn't want trouble down there (like, Austria is quite vocally unhappy with the arrangement) and likes to appear more a liberator than a conqueror for political PR reasons, so he decides that "Romania" is a brand new kingdom made of Moldavia and Wallachia, including Bessarabia (that's critical since Dobruja remains Ottoman) and gives it to, let's say, his brother Constantine.
This Romania is somewhere between Russia's close friend and Russia's puppet, and is bound to remain so, not only because the King is a Romanov but also having issues with both Austria and Turkey. However, kill a trillion butterflies for the sake of the scenario, and fast-forward a few decades (assuming a Napoleonic defeat and post-Napoleonic arrangement that follow the broad outlines of OTL, leading to a recognizable situation, although I admit that the POD does not grant that): Romania has been Russia's pal and maybe gained Dobruja and some other area in another Russo-Turkish war, whereby Serbia, Greece, and maybe a Bulgarian state have gained sort of independence with Russian aid (let's say that Austria is given Bosnia to sweeten the deal, though the Serbs are unhappy about it). The result is an alliance of Orthodox states in the Balkans that are friendly to Russia and very much make a point of being Orthodox, very very much so. Romania is somewhat senior in this group due to actual participation in the liberation of the others and dimension.
Constantine and his successors are generally a fairly reactionary bunch politically, but do some steps toward economic and infrastructural modernization and by 1850 there's some industry going.
The "Orthodox alliance", in the general pursuit of its "Orthodoxness" reaches out to Orthodox communities or something like that, but making fuss about the ones in the Ottoman Empire is very actively discouraged by a British naval squadron.
Romania, looking for a way to affirm itself on the international stage without much trouble and distract local hotheads from potentially unwieldy irredentism re. Transylvania, begins to send ecclesiastical, trading and diplomatic missions to Ethiopia, in cooperation with Russia and Greece of course but being the main drive. Relationships with the Ethiopians are actively sough after by the Romanian government and church as a matter of prestige. However, protecting the increased Romanian presence in the Horn proves tricky and, instead of abandoning the whole venture after the first few incidents, a small military presence somewhere on the Eritrean coast is established through the agreement of some local chief that has a nominal alllegiance to the Ethiopian crown, over Ottoman protest (the Ottomans claim suzerainity over the area, maybe outsourcing it to Egypt like IOTL, though not necessarily).
An uprising in, say, Macedonia sparks another Russo-Turkish war vaguely mirroring OTL's one in 1877-78. Romania of course is in on the Russian side. The Ottomans are defeated again, not crushingly maybe. Romania sees the opportunity, and decides to throw a demand for a stretch of Red sea coast at the peace table. The Ottomans care more about the Balkans and anyway they don't actually know what to make of much of their claim on that coast, that mostly theoretical anyway.
Egypt is like OTL with enough of a debt problem that it sells its own right on the area to Romania for some hard cash without much of a problem.
Romanian Eritrea* for you
* Probably significantly smaller than OTL's Eritrea, I guess it's only the coastal strip north of the Gulf of Arafali and maaaybe as far inland as Keren, or not even there; it may stretch a little beyond the borcer with Sudan, tough).