On screen there is nothing to suggest they can't, given the existence of the Doctor's granddaughter, Susan, and the Doctor has admitted to being a father. In the Virgin books, things get complex with suggestions that Time Lords procreate using "looms" (most notably "Lungbarrow" (novel)) but this has yet to be reflected on screen. (NB: questions regarding what is and isn't canon are beyond the purview of this site.)
Time Lords have been shown as children in, for example, "The Sound of Drums" (the Master as a child) & "Listen" (the Doctor as a child). Also, in "The End of Time", the Doctor & the Master reminisced about their childhood friendship.