I am the Mouth of Sauron.

[Legate of Amon Lanc]

Originally Posted by The Might

Hmm, here I must disagree...
I doubt he would have been very much perceived as "one of their own", but probably more like a traitor. Only people like the Dunlendings would welcome him as the new regent of that area.

I don't think Lal referred here to his assignment as "Regent of the West", but to the diplomatic mission between the nations. And from my thinking, for this he was certainly a good choice. Especially because of that most of these nations were probably Easterlings and Southrons, which I think fit into that "Dunlending" cathegory.
And with the Mouth being the "Lieutenant of Isengard" - I think it would be fine as well for him. The keepers of Isengard were always performing (or suspected of performing) sorcery, so he would fit nicely into the line. And I can imagine him as typical Roman-province prefect, of course serving to Sauron he would be very cruel and also really wicked, but just in person much like for example Pontius Pilatus (who, according to Flavius, has executed some pilgrims just preventively "what if they were rebels"). There would be rebellions, of course, but when raised, quickly bloodily prevented. The people would not like him as their lord, of course; but it would be a lot easier for the Dunlendings or some collaborative Rohirrim to associate with someone of their own kind than with an Orc, for example.