Not really, but there are alternative methods to get the same result.
You could, to name one example, put two copies of your field on your layout on different panels of an invisible slider or tab control. One copy of the field can specify the value list that you want for Browse Mode and the other can specify the value list that you want for find mode. Changing to find mode can also use go to object to change panels.
Or you can set up a global "search field". This can be accessed via a custom dialog, a modal new window or in a popover. You enter the search criteria that you want into this different field while in Browse mode and then a script takes this data, enters find mode, sets up the needed search criteria in find requests and performs the find. See this thread for example scripts: Scripted Find Examples
I use the same value list in Find and Browse mode all the time and the relationships do apply. I usually set up the field as a popup or drop down list. As a matter of fact I have several of these that can only be entered in Find mode. Could be I'm not understanding the question.