What do you mean by "initialize all memory"? This is probably only possible on some bare metal embedded system, not in Linux. And even there gdb does nothing like that.
Each program has two relevant special memory regions: one is zero initialized, which of course needs to be filled by zeros. This variables are allocated withing region marked as such and their value is not stored in executable. Other is initialized to some explicitly defined value. These values are stored within executable.
While it should be possible to get boundaries of this region (just like C library code does), the question is, why would you want to fill zero initialized region with NaNs. It would cause unwanted side-effects elsewhere in your code. For example, if you have some global int that is initialized to 0, filling this region with NaNs would also change the initial value of that integer to something entirely unexpected.
If you need some variables or array initialized to NaN, just initialize variables appropriately when declaring them (as explained by Notinlist and Rafael). You could use some macro(s), if you really don't want to repeat that ugly long statement every time, something like
#define NaNdouble(X) double X = std::numeric_limits<double>::quiet_NaN();