No. Resultant index will be single index but with compound key.
KeyX = A,B,C,D; KeyY = 1,2,3,4;
Index KeyX, KeyY will be actually: A1,A2,A3,B1,B3,C3,C4,D2
So that in case you need to find something by KeyX and KeyY - that will be fast and will use single index. Something like SELECT ... WHERE KeyX = "B" AND KeyY = 3.
But it's important to understand: WHERE KeyX = ? requests will use that index, while WHERE KeyY = ? will NOT use such index at all.
The most common implementation of indices uses B-trees to allow somewhat rapid lookups, and also reasonably rapid range scans. It's too much to explain here, but here's the Wikipedia article on B-trees. And you are right, the first column you declare in the create index will be the high order column in the resulting B-tree.
A search on the high order column amounts to a range scan, and a B-tree index can be very useful for such a search. The easiest way to see this is by analogy with the old card catalogs you have in libraries that have not yet converted to on line catalogs.
If you are looking for all the cards for Authors whose last name is "Clemens", you just go to the author catalog, and very quickly find a drawer that says "CLE- CLI" on the front. That's the right drawer. Now you do a kind of informal binary search in that drawer to quickly find all the cards that say "Clemens, Roger", or "Clemens, Samuel" on them.
But suppose you want to find all the cards for the authors whose first name is "Samuel". Now you're up the creek, because those cards are not gathered together in one place in the Author catalog. A similar phenomenon happens with composite indices in a database.
Different DBMSes differ in how clever their optimizer is at detecting index range scans, and accurately estimating their cost. And not all indices are B-trees. You'll have to read the docs for your specific DBMS to get the real info.