The answer to your question probably comes down to "Read the small print!", as policies will vary.
However if your policy covers damage due to flooding/water incursion then, yes, you can probably claim.
As a general legal principle, the clock starts running on time-limited claims from the time that it becomes apparent that there's a problem and not from the time that the problem actually occurred. (e.g. someone who worked for a company where there were asbestos fibres in the air thirty years ago, and who has just received a diagnosis of asbestos-related cancer, isn't prevented from claiming against the company on the grounds that the damage to his lungs occurred back in 1990 and is therefore 'out of time'. The clock only started running on his ability to claim from the day he received the diagnosis).
Similarly, the clock on any claim you might have against the insurer only started running from the moment that you first noticed that there was a problem, even if it can be shown that the actual cause is a very slow leak that's been there for years. However, unlike my asbestos-related example above, the time limit on insurance claims is often quite short (such as 14 days), so don't hang about when it comes to submitting a claim.
As long as everything contained in a claim is true (i.e. you're not seeking to defraud the insurer) then the rule is "If in doubt, claim!". The worst that can happen is that the insurer will find a reason for rejecting the claim, whereas the best is that your claim will be settled in full.