Will this SN1 reaction result in an equilibrium situation?
Thinking about the SN1 reaction generally, we know that the rate is first order, being proportional to the rate of decomposition of the C-LG bond of the reagent, with the identity/concentration of the nucleophile being completely irrelevant. Your issue, therefore, becomes one simply of the relative leaving group ability of water vs chloride. 

Quantitatively, you could think about this on an energy diagram (below). For both the forward and reverse reactions, there is an intermediate carbocation (formation of this is rate limiting), once this carbocation forms there is then a fast recombination of cation with a nucleophile to form a 'stable' species. So, in essence, absolutely the reaction can go in both directions, but in practice often goes in one direction (actually microscopic reversibility dictates that this is almost always the case, but the energetics of one direction are such that reactions aren't realistically reversible). 



With respect to your actual example, you might like to take a look in Clayden/Warren, Organic Chemistry. The actual example you're interested in is discussed, along with a discussion of relative leaving group/nucleophile ability. 


  
  
  Ref: Clayden/Warren, Organic Chemistry. 




As a general side point, the website you cited isn't great. There are many errors and general mistakes. You'd be far better looking in a textbook (theres a meta post with good suggestions if you're interested).