I believe plants are routinely stored at local shops for a week or two. Add to that transport from the manufacturer. So, a few days are probably safe. After that, no guarantee. It depends on many variables.Do you have a rough estimate of how long they will survive?
Majority of hobbyists (incl. here on UKAPS) recommend planting as many plants as possible at the first strike. The reasoning goes that a huge mass of plants would overcome the adversities of a new tank easier.Ideally I would like to place them in my tank all at once, rather than add them as they arrive.
I - again - represent a minority voice. I've got my doubts about it. I believe that re-planted plants need time (a few days, a week, some even longer) before they overcome their own difficulties and their contribution to the tank's environment turns net-positive. Par example, a few days after re-planting they respire more than photosynthesize. (This is not my idea, I've read some scientific papers on the topic.) I'd describe this situation as introducing too many patients and no doctors.
I think the truth is somewhere in-between. Floating plants are likely to adapt faster. Also, often recommended "undemanding fast-growing stem plants" recover quickly and turn from patients to doctors. On the other hand, there are good reasons not to hurry with introducing more sensitive plants - both sensitive species and individuals, like tiny plantlets from tissue culture.
In short, I don't think that "planting straight as many plants as you can" is a universally valid rule which you cannot break. A more nuanced approach may lead to better results.