If this is your security mechanism (chuckle), then attackers will just slow themselves down by duty cycling. Say, only attacking for 100ms at a time, then sleeping a second. You'd never know.
...making it even more unlikely the attack would find anything of value (or even recognisable as such) in a reasonable amount of time.
To use an analogy, these side-channel timing attacks are really a "looking for a needle in a haystack" (or heap...) situation, except that [1] you don't necessarily know what a needle looks like, and [2] the haystack is constantly changing. AFAIK all the PoCs shown so far relied on having a deep knowledge of the system and carefully constructed conditions.
If these attacks could undetectably dump all of your RAM in a few seconds, that would definitely be a huge concern. But they're more like being able to read a few bytes per second, from somewhere in the address space, with no idea what they are or where they're being read from, and no guarantee that they're even contiguous.
