No. Albanians are a Balkan European people; they are not an Arab ethnic group. Encyclopaedia Britannica describes Albanians (who call themselves shqiptarë and their country Shqipëria) as generally considering themselves descendants of the ancient Illyrians of the western Balkan Peninsula, with Albania located in southern Europe on the Adriatic.
Their official language, Albanian (shqip), is an Indo-European language in its own branch of that family. Arabic, by contrast, is a Semitic language that originated on the Arabian Peninsula and is spoken across North Africa and much of the Middle East. Centuries of Ottoman rule left cultural and religious influences in Albania, but that history does not make Albanians ethnically or linguistically Arabic.
Source: Albania — Encyclopaedia Britannica (and Arabic language — Encyclopaedia Britannica).