語源由来辞典 lists theories that they might be connected for the very same reason you mentioned, among others.
動植物が腐ると悪臭を発することから「くさあるる(臭荒)」とする説もあるが、「くさい(臭い)」は「くさる」が語源なので、前後関係が逆転している。「くそある(糞生)」から「くさる」に転じたとする説もあるが、「くそ」も「くさる」もしくは「くさい」から生じた語と考えられるため、この説も採れない。
The way I understand it, it is generally believed that 腐る, along with くそ, stems from 腐る, but that is not proven (and there are other conflicting theories, such as 腐る stemming from 糞荒【くさあるる】, whose reading I can't quite explain).
Apart from that, I've been able to retrieve two related citations from the 岩波古語辞典, from two different sources.
The first one is for 腐り, from a Yahoo! question.
「クサシ(臭し)・クソ(糞)と同根。悪臭を放つようになる意」
The second one is for 臭し (classical form of 臭い), which can be found here.
<クサリ(腐)・クソ(糞)と同根> はげしい、いやなにおいがする。悪臭を放っている。
As you can see, both entries cross-reference each other.
So, it seems like the 腐る・臭い connection is definitely the most agreed upon theory, although there does not seem to be a definite proof. There definitely seems to be some kind of connection between (at least two of) くそ, くさい and くさる, though, although we can't know for sure how exactly it's laid out.