Ice crystals are formed 'depending on environmental temperature and humidity, .....' It shows that crystallization depends on molecular interactions in this case. How we will define bond energy if we remove the parameters T and P. What do you mean by 'bond strength of a growing crystal?' But thanks for this question.
According to the supramolecular synthon concept, there is a relationship between the bond energy of interactions and their priority. The relationship is also quite opposite to what you assumed "i.e. can an assumption be made that lower bond energy may cause fast growth rates in crystals if all the other parameters are kept constant". On the contrary to your assumption, the most frequent bond which is energetically strong with proper geometry can be formed as the primary supramolecular synthon. Afterward, the secondary synthons presumably will be formed. This is just a microscopic driving force for crystal growth and its correlation with macroscopic evidence was not fully explained, yet.
However, if you are going to understand the process of crystal growth you need to study some concepts such as prenucleation clusters, polyamorphism, nucleation and etc.