Potential Advisor offered to write "note of support?"

[GreenVase]

Have been corresponding periodically with potential advisor and met in person during a campus visit. This person told me to let them know when I applied and that they would write a "note of support" for my application. Is this common? I assume it's like an additional reference letter, except obviously less detailed and not based on an extended knowledge of an applicant's previous work? I don't think this person is on adcomm this year (given that they'll be on leave), but is a senior scholar who's one of the biggest names in the department. So it's a good sign, right? 

[Aghhhhh]

I have a 4th LOR who basically offered the same thing! At first I was hesitant, because I wasn't sure how a brief, positive letter might look to admission committees, but my mentors all encouraged me to take him up on the offer. First, anyone that goes out of their way to offer a letter (or note) probably thinks very highly of you and they'll reflect that in their writing. Second, what is the harm in having an additional positive letter?

Now if this person was one of your main LORs, I would think about how the brevity of his note could be perceived, but if it's just an additional letter, I'd say definitely go for it.