Is regeneration a mediate or immediate work of God?
At first I thought you were asking whether regeneration was monergistic or synergistic.... and that answer is obvious - it is monergistic, a work of the Holy Spirit. This is absolutely the case and any discussion of any instrumental cause in regeneration needs to bear this in mind. God and God alone regenerates.
As to your question: the best answer may be "yes".
Normally, the Spirit works with the preached word of God - so in that sense it is a mediate work. Peter clearly brings this point out in 1 Peter 1:23, and James in James 1:18. Paul also argues this way in the familiar passage Romans 10:14-15. (having also dealt with the power of God in the Gospel in Romans 1) Hence regeneration apart from the Gospel preached is hard to conceive of Biblically. Regeneration precedes faith logically, but a strong argument can be made that they are "bam-bam", i.e. that those regenerated by the Spirit of God exercise faith as they are regenerated. Such faith requires an object, and that object is provided by the Gospel truth preached.
That said, the preached word is not a guarantee - for it is effectual only upon the elect hearer. God acts as He will, regenerating the heart of His elect when and how He desires. Some come to faith at the preached Gospel - others, not elect, never will no matter how much the Gospel is preached to them. For many, I think, this is sufficient reason to argue that it is an immediate work of God, apart from the preaching of the Word. I don't think that's necessary, but it is something that many will argue.
In any case, the existence of an instrumental means, such as the preached Word, in regenerating the elect does NOT mean that regeneration ceases to be monergistic. That it is, and that, surely.