Even before I could look at a dictionary, I told him that it wasn't likely, since I remembered that while erusin with the letter samech is the form in Rabbinic Hebrew (and followed in Modern Hebrew as well), in Biblical Hebrew it is spelled with the letter sin - ארש.
But when I looked at Klein's entries for the two of them, I discovered some information I did not know previously.
Here is what he writes for ארש (having noted in the entry for ארס that these are variant spellings), with the meaning "to betroth":
Among the many attempts to find the origin of this word the most probable is the one which connects it with Akka. ērishu (= bridegroom), irshitu (= betrothal), which, according to Haupt, derive from Akka. erēshu (= to desire) ... cp. also Arab. ‘arus (= bridegroom).
He then connects this root to the word areshet ארשת. I knew the word areshet well from the prayers on Rosh Hashana, sung after the shofar is blown. But I'm a little embarrassed to say I didn't actually know what it meant. Here's what Klein writes:
expression (a hapax legomenon in the Bible, occurring Psalms. 21:3 in the phrase אֲרֶשֶׁת שְׂפָתָיו, which is usually rendered by ‘the request of his lips’. Most Jewish commentators, however, render אֲרֶשֶׁת שְׂפָתָיו by ‘expression of his lips’. [Prob. related to Akka. erēshu (= to desire), erishtu (= desire, request).]While erishtu meaning "desire" is similar to the Greek erasthai meaning "to love, desire", and is the origin of the word "Eros", I have not found any sources that connect the Greek and Akkadian words. I also have not found any sources that connect the root to the Arabic ars, which meant "pimp", and entered Hebrew slang as a derogatory term meaning someone low-class and sleazy.
Stahl, in his Arabic etymological dictionary, in the entry for arus (bridegroom) says that this root might be related to arisut אריסות - "tenant farming, sharecropping" and aris אריס - "land tenant", since the transactional nature of leasing land was similar to the dowry involved in marriage. However, Klein provides a different etymology, connecting it to the Akkadian erēshu (= to till the soil). That makes it cognate with the Hebrew kharash חרש - meaning "to plow."
And what about eres meaning venom or poison? Here is Klein's interesting entry. He says it was a post-biblical word:
From earlier אִירָס. Of uncertain origin. Perhaps, together with Syr. ‘irsā (of s.m.), a blend of Gk. ios (= poison) and L. vīrus (= poison).
Eres and "virus" are so similar, I'm surprised I never thought of a connection before.