Does it make sense to choose skill speciality at skill 0 instead of skill 1?

The most important effect is to not have the -3 for no skill. +1 is relatively substantive in a 2d6 system, so it does matter. But your characters are not crippled by not having a Rank 2 or Rank 3 skill mechanically. Traveller is designed around most modifiers being in the 1 to 3 range.

From an RP perspective, Rank 1 is professional competence, while 2 or 3 is increasing degrees of expert. So if your player wants to be an acknowledged expert, ideally they'd have a higher skill rank.