Can the common algorithm to convert to Chomsky Normal Form result in “useless” productions?
Given a $CFG \ G$, before converting in $CNF$ you need to clean the grammar, that means (order is important):


  1) eliminate $\epsilon$-productions
  
  2) eliminate unit productions
  
  3) eliminate variables that do not derive terminal strings
  
  4) eliminate unreachable variables from the starting symbol


After this you make substitutions/split rules in order to obtain a CNF grammar.

According to these rules, after your step 3 I would eliminate non generating variables (all the variables can reach a terminal string) and unreachable variables (You cannot reach $S'$ from $S$), to end up with the following productions:

\begin{align*}
  S'\!\!\!&amp;\longrightarrow a\,|\,aX\,|\,Yb\\
    \ X&amp;\longrightarrow a\,|\,aX\,|\,Yb\\
 Y&amp;\longrightarrow bY\,|\,b
  \end{align*}

I don't know which procedure you are following (it may vary according to textbooks/instructors), but if you don't apply steps $3$ and $4$ then yes, you could end up with useless symbols in your grammar in CNF.