I really cannot answer your question for sure regarding if absinthe was offered on Titanic. I can only speculate.

It seems to me that since absinthe had kind of a bad stigma labled to it in the early 1900s (like rumors of making men go crazy and killing their families), that if would be seen by "polite society" or the guilded age not to be a proper beverage (not compared to brandy or conaqe).

But then again, this is only speculation, do not take my word for it.

If you do not get a list of the alcohol they served on Titanic from anyone on the web, you might want to look at a bookstore for a book called "The Mammoth Titanic Book". I have heared reviews that the book is very detailed when describing its cargo (So much that your average beginning Titanic student is bored while reading it).