Regarding SEVEN people on a MONTAUK working "great": not really.
In a MONTAUK 17 the seating would be good for two people, who would sit at the helm side-by-side, in either the reversible pilot seat or on two molded swivel seats. Two more can sit in front of the helm if there is the optional cooler with a cushion seat added to the boat, but adults sitting on the cooler seats will tend to obstruct the view to the people at the helm, particularly the helmsman, who would have to stand to see over them.
To create three more safe seats for small children you will need to improvise. One possible solution might be to add a full-with bench seat behind the helm seats. In Figure 2 below you see a nice MONTAUK 17 with an owner-added seat in the aft end of the cockpit.

- Fig. 2. An overhead view of a classic MONTAUK 17 which has the cooler seats forward of the helm, a reversible pilot seat at the helm (both options), and an owner-added third seat. Note how there is no seat back at the stern seat on the port side. That allows people to reach the boarding ladder.
- Montauk17overhead.jpg (69.24 KiB) Viewed 19310 times
The effect is to convert a wonderfully open and enjoyable small center console into a crowded school bus.
The specifications from Boston Whaler list the capacity of the MONTAUK 17 as seven persons. So, yeah, it is legal to have seven persons on board. However, to keep it legal you will need to have seven USCG-certified personal floatation devices on the boat, one for each of the seven people and appropriately size for the person who will wear it. Also you need an eighth flotation device on board, a USCG certified throwable device, often a floating cushion. And you will need a fire extinguisher, fenders, mooring lines, distress signals for daylight and darkness, and perhaps a few other safety devices to comply with USCG and state regulations.
Then for the engine you need a fuel tank, maybe an oil tan, and a battery.
All this gear goes on deck, or inside the center console, or in the cooler (if you are not using the cooler to keep drinks cold).
Also, most people who go out on a boat usually bring along some extra stuff, like maybe a swim suit and towel, maybe a jacket or rain gear, maybe even a bag for their purse or wallet or cellphone or camera or other stuff. It is very unusual for people to just come aboard with nothing. More gear takes up more space and adds more weight
Where is all this stuff going to go so that your cruise will "work out great"?
A small boat like a MONTAUK 17 is relatively light. The performance will always be in proportion to the power-to-weight ratio. When seven people are aboard the total boat weight will increase significantly compared to having just one person on the boat. Even in the best case where all your family is very fit and weighs at or below the "average" weight, three adults are likely to weigh a total 450-lbs or more, and three children are going to weigh at least 150-lbs or more, so the boat weight is going to increase by at least 600-lbs--and likely more than that.
As a result of the weight increase, the response of the boat to increase in engine throttle is going to be more sluggish, and there is a possibility that boat may struggle to even get on plane, depending on what engine power is available. The way the boat will handle and feel to the helmsman will be quite different than with a light boat load.
Also, if you plan to leave the MONTAUK 17 on "a float" (which I infer means on a mooring in tidal saltwater) you will need to protect the hull with an epoxy bottom coat and then an anti-fouling bottom coat.