I'm an 90% sure of this answer: No.
You are looking to detect if you are on a browser that looks weird
but you are defining weird
subjectively. User Reda's answer is correct, but it violates part of your question (not to identify browsers by name). My point is that you need to identify the browsers by name because you're qualifier is subjective, so you won't find a JS/CSS test for it.
Browsers have complete control over what dropdown they show. Most are inconsistent with their implementation of CSS on these dropdown components. There are no standards saying a browser needs to expose any information about the dropdown at the application level.
To affect what you want, you need to find the browsers whose dropdown controls you don't like and list them out, and target them via Modernizr or other such trickery. Unfortunately that violates your question's intent, so I think the answer to your actual question is... no, sorry.
window.orientation
? Maybe all those mobile devices nowadays do display a nice and usable native select (multiple or not) control? – Mulry