I hope to be able to help answer your question today.
If the police get behind you and run your plates, however, they will not be able to know that you have purchased and are awaiting the sticker/plate. The only information police would have is that the plate that they ran comes back as expired. Generally, police do not randomly run license plates while behind someone unless there is a reason for them to do so (i.e., speeding, car accident, or any other traffic violation proceeding the run of the plate information).
In situations like this, because the offense would be very minor (a traffic infraction), if you were stopped and ticketed by police and given a court date, if you appear in court with the documents that shows you applied and paid for the sticker prior to the date you were ticketed, the prosecution would most likely dismiss the case. This is especially true if the standard operating procedure in Indiana is to mail the sticker/plate.
Now, if you purchased the sticker/plate after your plate had been expired, you will end up in the same situation. However, the prosecution may or may not dismiss the case because you technically purchased the sticker/plate after the time you should have. In smaller areas, this is more likely. However, in larger areas where prosecutors have more cases to deal with, they may still dismiss the ticket, especially if you do not have an extensive criminal or traffic history.