What do you mean by "searchable", exactly? How would you like it to behave?
I know that this is an old thread, but I have a similar question in regards to creating a searchable drop down list in Live Cycle Designer. I'd like the choices in the drop-down list to narrow as additional characters are entered in the text box, until the user clicks a choice or only a single choice remains. The search can be for initial characters rather than for anywhere in the string, but should ignore case, since all characters in the choice list are upper-case alphanumerical, with a period -- then followed by a description. (e.g. "M22.2X2 Patellofemoral disorders, left knee" or "M22.2X1 Patellofemoral disorders, right knee".)
Using a text box to emulate a drop-down list, I couldn't position the next form element higher than the bottom of the list box. Using a regular drop down object, I got further than single-character search, but the first list item matching user-entered characters would end up selected even if a different item was clicked in the drop-down list. Additionally, in attempting to ignore case, I'd end up with the destructive backspace or delete keys not working, which prevented entry error correction.