I would say no.
For legitimate or non-legitimate reasons, the hiring manager has not gotten back to you. That's okay.
A company that wants to hire quality people and that isn't stuck in a morass of mismanagement and red tape will be able to make you an offer fairly quickly. As in, within a day or three.
Years ago, I was flown out to
[city] to interview at
[Acme]. On my own, I arranged for an additional interview at
[Frobozz] later the same day. I originally wanted to work for Acme and thought of Frobozz as a backup. Frobozz made an offer that very day. I accepted, because a bird in the hand, etc.
Three weeks later, Acme made an offer. I gently turned them down (no sense in rubbing their face in it). Ironically, years later Acme was bought by another company and both tanked.
The point is that on that day, I had one offer from Frobozz and no offer from Acme, so the choice was obvious. Right now, you have no offer. You can pursue this non-offer, or you can look for that company that wants to hire you today. Which choice makes the most sense?
*Never, ever apply at only one place and think your work is done for the day. Why? Because you don't even know if that company even has a position and/or budget! I've had several verbal offers over the years that evaporated because budgets changed, reorgs happened, etc.