No, usually the models are fairly well structured with enough support to compensate for the extra weight, if any at all. Those that potentially to have a weight problem usually have supports anyway because of the type of model they are (example; figmas).
Garage kit model, however, are a different story and may topple over due to being cheap and poorly designs. Though not all resin kits are made out of poor designs and it varies per producer.
Apart from this the only ones likely to have any problems are the cheap China/Hong Kong/Korea bootleg productions which have more faults to worry over then weight issues.