Yes, but your fans would start spinning like mad. I kill any browser that does that. You’d have to execute a successful attack within a few seconds to pull it off. I think that’s a risk I’ll take.
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.
Good lord, I hope this is satire.