Yes, to an extent.

Both are Semitic languages, but belong to different branches - Aramaic is a Northwestern Semitic language (a group which includes Phoenican, Amorite, Ugaritic which are now extinct and Hebrew).

Amharic on the other hand belongs to the South Semitic branch and more specifically Ethiopian further dividing the group.

Neo-Aramaic languages spoken today (mainly by the Assyrians) are Neo-Assyrian and Neo-Chaldean as the two major ones. The group also includes Surayt/Turoyo.

Are Amharic and Aramaic intelligible? No, they aren’t.

For example, every dialect of Aramaic has its own pronounciation - and most of them lost the empathic consonants which some other Semitic languages (such as Tigrinya and Amharic) have. Aramaic also borrowed words from languages such as Azerbaijani, Turkish, Persian, Arabic and Kurdish.

They also have many features they share (mainly grammatical) but there are also differences (vocabulary, loss of some features in Aramaic and so on). And the obvious difference is the different writing systems - Aramaic is written using the Syriac alphabet, while Amharic is written with the Amharic Fidel which developed from the Ge’ez script.

Syriac alphabet

Amharic Fidel