As expansionistic as Imperial Russia was, I just can't see them trying to occupy the whole OE.
First, they had already agreed to the partition of the OE in the Sykes Picot Agreement and surely Great Britain and France won't be happy campers on getting booted out.
Second, Russian leadership was already concerned about the large number of non-Russians in the Empire. About 75% of the OE's population was Muslim, at the beginnning of WWI, that means about 15 million Muslims, and another 5 million or so, Greeks, Armenians, Bulgars, etc. This would about double the number of Muslims in the Russian Empire, that's asking for trouble.