How many bits to represent a quantity $\omega$ bounded in a particular way?
Yes it's correct, but I would not introduce the rounding until the end. Let $w = |\omega|$, then in the worst case:

$$w \leq \rho r^{k+1}y$$

$$w \leq 1\cdot r^{k+1}y$$
$$w \leq (2^l)^{k+1}y$$
$$w \leq (2^l)^{k+1}(2^k-1)$$
$$\log_2(w) \leq \log_2((2^l)^{k+1}) + \log_2(2^k-1)$$
$$\log_2(w) \leq \log_2(2^{l(k+1)}) + \log_2(2^k)$$
$$\log_2(w) \leq {l(k+1)} + k$$
$$\log_2(w) \leq {(l+1)(k+1)} -1$$
$$\lceil\log_2(w)\rceil \leq {(l+1)(k+1)} -1$$
$$\lceil\log_2(w)\rceil &lt; {(l+1)(k+1)}$$