Spot on, though that still has to count through the order tree. This is functionally identical:
SELECT id FROM table1 ORDER BY id DESC LIMIT 1
... and may run faster despite the more complex query since it will use the existing index. I think that's what Litebearer was suggesting.
Unless of course need that exact query because you're showing all of those results AND need to know the last ID... if you were using mysqli instead of mysql commands, you could seek to the last result, pull it's id, then seek to start rather than run a separate query. in PDO you could fetchAll letting you process it as a normal array (the last() command would be handy then) -- just be sure in that case to release the statement object so it's not hogging memory.