Not really, no. That runs counter to the fundamental winforms model. You can probably cheat with a lot of manual munging or interop, but that would hardly be worth the cost.
Instead, ask yourself why you're doing this. It looks like you're trying to reimplement a combobox for the sole purpose of adding autocomplete. Perhaps you should simply subclass the combobox control to add your autocomplete functionality to the control that does all the hard stuff for you and already exists.
In the course of my current job, I've seen at least three different home-grown comboboxes that were all broken in various ways, amounting to a lot of work with no real payoff. My favorite was the combobox whose dropdown listbox stole the owning forms focus. It was really funny watching the broken code cause anything that used it to flicker.
Edit:
Modifying the combobox to be a search/filter with wildcards is still possible via inheriting from ComboBox, and still easier than rolling your own combobox, but at that point I'd suggest considering a more appropriate ui paradigm. Comboboxes don't filter their drop-down list (unless you use lousy software as inspiration coughSAP*cough*).