Sadly the simple answer is no - at least, not in the current production models.
As a rule of thumb, the current models can be identified as follows:
Base - manual - no seconds - no date - exhibition back (except the LOGO models)
Marina - manual - small seconds - no date - exhibition back (except the LOGO models)
Marina Automatic - auto (!) - small seconds, date - solid case back
This obviously doesn't exclude the fact that earlier models (and/or SE) were made with 'subtle' differences - ie; an exhibition back here, a date there...
Generally, to get a date, the watch must be an auto movement - but this isn't a hard and fast rule either! That's what makes it so interesting/frustrating...
I have a PAM00253 Regatta and whilst I love it to bits, it hasn't got a date - despite the fact that I have a date on my computer, my portable telephone etc. I feel more comfortable when I have it on my watch too.
To complicate matters even more, my current 'love' has a whoping 10 day power reserve
and it's an automatic movement!! Talk about confusing...