Thanks Tom.
While it seems that search engines generally handle these characters well I still had to ask because I did two Google searches: One for "lole" and another for "lolë", and I got very different results. On the first search my website came up on SERP page one but on the second one we were nowhere to be found on any of the first 15 pages.
Whats more, every one of the first 10 SERP pages or so contained at least one instance of the character with an accent in the title, description, or within the on-page copy. So it seems that special characters and regular ascii characters are not one in the same, or at least they are not weighted the same.
I do have to agree with you on the fact that most users will not go through the trouble entering Alt codes on their search bars. On the other hand, the fact that we barely register on SERPs for the company's DBA name might be cause for some concern.