Cons--Inject foam into air voids and you ensure that, if any water does get in, it will never dry out, meaning things will rot quicker.

Pro-- If you do develop a major leak that fills up those air spaces that should act as flotation, the foam may keep you afloat. Your call.

Will quiten the hull down as well, no issue if your stringers are foam composite or box section glass rot wise though, as ranmar said timber stringers will rot from the moisture in the foam in this case you could flowcoat the stringers to seal them up as bare Fibreglass is pourous otherwise. 

might sound stupid but one of the boat builders fills the underside of the flooring with foam pool tubes or noodles , I bought out a few shops when they were cheap and filled the under side of my alli boat and certainly quietened it down , allows water to pass through and they can be removed when required, injected foam or foam fill can get into areas and when it expands can cause issues so be wary if doing that option

Pool noodles are porous and will absorb quite a bit of water and become heavy - they still float but not as well. Used to leave them in our pool to keep the cover suspended and they would become quite waterlogged so not ideal for boats imo. I wouldn't be happy if I found that after buying a boat from a builder. If you do it yourself each to his own but beware of the extra weight if water gets into them.

The proper two part mix expanding foam can cause damage (such as buckling floors) when it expands if your not careful but only if it doesn't have another avenue of escape. Couple of well placed cookie holes to be covered/patched after foam mixture expands alleviates this.

 I was going to use Pool noodles in my dinghy, the idea sounds great but I had a couple in the shed up north here and the heat of one summer turned them to powder. Went to use them and they disinergrated in my hand. 

I had the two part mix put in my baron sportsman when I had the floor redone a few years ago. Definitely quietened it down, no buckled floor. I definitely feel alot safer when I'm 20mile out

 Approved method

  Nice topic ,What I did was put marine foam blocks in my boat, got my hands on sandwich bread trays which are plastic creates and cut them down to size to fit hull then put foam block on top still allowing air flow between hull and foam 

 a nice cheap alternative is empty coke bottles 

 My boat  has been rebuilt with 30 mm Klegecelll pvc foam stringers I have poured 2 pack foam in to the forefoot of the hull back to the forward bulkhead then glassed over the top it will sweat and still hold moisture though this along with fully sealed chambers in the floor will keep her afloat by the bow section if anything goes pair shaped.