Yes, it is, without question, although it is a different kettle of fish from FTF gaming, certainly.
PBEM is roleplaying in a literary vein. Arref does have a good point, the storysetting is harder to get across in words sometimes than in gestures and actions in a FTF role. I will give my over-the-top depiction of the death of King Oberon in IT's A Mad Mad Mad Amber as an example--I could not have done that in a PBEM. PBEM sensibilities are filtered through words and only occassionally images and other media.
It is roleplaying though...since I consider letter games such as De Profundis to be roleplaying, or things like the quiescent Bete Noire. Granted, it takes players and GMs who can write and like to write. There is nothing more frustrating for me than a GM to get a one word or one line answer from a PC...it kills my roleplaying mood like almost nothing else. On the other hand a lack of time can halt a PBEM game in its tracks. There is almost a presumption of flow in a PBEM, when it is violated by the GM or the player, the "shared space" of the game disintegrates. I try hard on turn turn-around and when players drop off, my interest in their part of the constellation of my game fades, too.
I do love and will steal Arref's definition of RP:
Roleplaying is a parlor game where Players choose Characters that will react to the presentation of a Storysetting by a Gamesmaster. The improvisation of the Characters (and Gamesmaster) determines the outcome of conflict and events.
I would amend and extend it as follows:
That form of the parlor game can take in a variety of "parlors" and media, ranging from Live Action Role playing, through face-to-face "tabletop" roleplaying, to PBEM games, to "letter" games, in which the latter have a virtual rather than an actual shared space, and the values shade from the Acting of LARP over to the Literary.