Yes, it is possible to crystallize HAP from a precipitation technique. but it will be a primary nucleation, not homogeneous nucleation due the presence of the walls of the vessel that induces the formation of the solid. Homogeneous nucleation in crystallization systems is more difficult to happen. Both are stochastic process that means you cannot control or reproduce it well.
See
Influence of process conditions on hydroxyapatite crystallinity obtained by direct crystallization
Dear Panagiotis, thank you for posting very his interesting technical question on RG. In addition to the relevant literature reference suggested by SILAS DERENZO please also have a look at the following potentially useful articles which might help you in your analysis:
Preparation of large-sized hydroxyapatite single crystals using homogeneous releasing controls
Article Preparation of large-sized hydroxyapatite single crystals us...
This article is freely available as public full text on RG so that you can download it as pdf file.