The simple answer is no, this misinformation has been around for many years and is what some pest controllers tell customers who are rightfully concerned that the use of rodenticides inside their home will mean a decaying rodent will be left behind.
The truth is that no rodenticide will cause rats or mice to leave a structure after consuming it. Rats do need to drink water, but the last thing on a rats mind after it has consumed a lethal dose of anticoagulant will be to go for a stroll down to the local rodent watering hole.
If using rodenticides indoors there is always the risk that the rodent will die somewhere inaccessible and cause a bad smell, but in reality it rarely happens. I have had rodents that could not be retrieved only a handful of times during my years working in pest control. I find temperature is the determining factor that causes a dead rodent to smell. If a rodent dies behind a cooker or laid across a hot water pipe the yes you will have an unpleasant smell and unless it can be retrieved it may last for a couple of weeks.
You are the customer, its your property and ultimately your decision. A point to consider is that rodenticide if presented correctly will often clear the infestation quicker therefore at a lower cost than if using traps. Occasionally rats will be caught within hours of set up however this is not the norm. Rats are generally very cautious around new or unusual looking things, this is called neophobiaextreme or irrational fear or dislike of anything new or unfamiliar. This is one of the reasons rats have become so prevalent, staying away from unfamiliar things keeps them alive.