Yes, on many occasions. This includes US actors (not always playing US characters) & US characters (not always played by US actors). Examples:
- In the classic series Peri Brown, companion of the Fifth & Sixth Doctors, was American (though the actor was not). A number of American actors guest starred, including Hollywood musicals actor Stubby Kaye.
- The 1996 TV movie "Doctor Who" was set in the US and thus had many American characters of a variety of ethnicities, though the film was actually shot in Canada and as such many of these actors were in fact Canadian, such as Yee Jee Tso and Will Sasso, though the key roles of Grace Holloway and the Master were played by Americans.
- In the revived series, the opening episodes of Series 6 "The Impossible Astronaut"/"Day of the Moon" were also set in the US & had many Americans, including President Richard Nixon (played by American actor Stuart Milligan). Ben Browder guest-starred in "A Town Called Mercy" and Mike McShane guest-starred in "The Angels Take Manhattan".
- Big Finish Productions has cast Americans in many of its audio dramas, including Juliet Landau as the new Romana, also known as "Trey", and Chase Masterson as Vienna Salvatori.
This isn't a complete list.