Does converting algorithms into elementary recursive form preserve runtime bounds?
This depends highly on the encoding.  If you consider bounded summation, the number of summations done is the value of the first argument of the function.

If the "encoding" (whatever that means) of the input is unary, this takes linear time, otherwise it takes exponential time in the size of the input. It is not obvious that it makes sense to assume input to be unary.

Elementary recursive functions are over natural numbers and do not speak of their encoding: is $s(0)$ encoded as $1$ or as $s0$?