Can I remove left recursion on this grammar
Yes that is correct. Also you can safely remove $A\rightarrow A$ type of production rules. So the equivalent grammar is $S'\rightarrow aS'\ |\ \epsilon$.

If you analyze carefully you will see that you are not applying Algorithm 4.19 at all. We are just removing left recursion where we have only immediate left recursion.

Cycles are of the form $A\rightarrow B, B\rightarrow C, C\rightarrow A$. When we remove left recursion in immediate left recursive grammars, we are ignoring $S\rightarrow S$. 

Also presence of $\epsilon$ creates problem for the algorithm 4.19 given in the red dragon book (2007 edition), but the method of removing left recursion in immediate left recursive grammar works even in the presence of $\epsilon$.