How to compute the output length of randomized encoding (or garbling)?
The size of the randomized encoding (or garbled circuit) produced by a given construction will be specific to that construction. (Indeed, there are major efficiency improvements to GCs/REs that are still being discovered every year.) So, to answer your (own) question, it would require focusing on a particular construction's details to answer fully.

However -- Yes -- it must be the case that any garbled-circuit / RE that is output by any probabilistic polynomial-time $\mathsf{Garble}$ or $\mathsf{Encode}$ procedure has size at most $\mathsf{poly}(1^\lambda, C).$ For the procedure to output something significantly larger, e.g. exponential in $1^\lambda$ and $|C|$, is impossible (in prob. poly time). Moreover, the typical constructions that come to mind -- e.g. Yao's Garbled Circuits and Applebaum-Ishai-Kushilevitz's randomizing polynomials -- have size approximately $O(\lambda\cdot |C|).$ (It's likely that whatever you're looking at is 'loosely in this range,' though schemes close to the state-of-the-art will have various fine-grained differences..)