As with many things in estate law, the answer is that "it depends." In certain cases, the answer is "yes" (but this also implies that in other cases, the answer is "no").
Section 733.304, Fla. Stat. provides that a person who is not domiciled in the state cannot qualify as personal representative unless the person is:
(1) A legally adopted child or adoptive parent of the decedent;
(2) Related by lineal consanguinity to the decedent;
(3) A spouse or a brother, sister, uncle, aunt, nephew, or niece of the decedent, or someone related by lineal consanguinity to any such person; or
(4) The spouse of a person otherwise qualified under this section.
If the person to be nominated as Personal Representative does not fall into one of the four categories listed above, then they cannot serve. This is true even if all interested parties are in agreement--the person simply is not eligible and cannot qualify.
In doing your estate planning, you should discuss this issue with your estate lawyer so that your Will has persons who can qualify as Personal Representative.