Late to the party on this one...
There are rare programs that have critical care fellowships for family medicine, however I am not aware of any that are ACGME accredited, and it is likely that if you did not train @ those programs you might be at a disadvantage in securing a spot. That being said, if the programs have made them financially sustainable it is definitely worth a shot and they would likely consider outside players if no one from their own institution was considering filling the spot.
While family medicine is a primary care specialty, family medicine encompasses more than primary care depending on the area of the country you are in. There are many places that would be excited to know that you want to do hospitalist work, and yes, would feel comfortable managing your patients in their open ICU, vent management and all. Granted this would not be in most of your urban centers. And your luck is best found west of the mississippi.
Family medicine residencies run the gamut of having 0 ICU exposure (in spite of the RRC requirement to follow 10 patients) to spending 3 months of dedicated block time in a closed ICU (the latter being much less common).
As far as family docs that have done ICU care without a fellowship, I am aware of some that have done this; but normally after a period of preceptorship and with appropriate backup-- whether it be pulm, anesthesia, etc.
If looking for that, it might be best to find a more remote/rural hospital with an ICU understaffed by intensivists desperately looking for someone to take the burden of some call off their shoulders. This might mean you get precepted for months, where you run every admission by them, and then gradually only call them when you need support. You would be more attractive to a group like this if you already had reasonable hospitalist training and felt comfortable with arterial lines, central lines, and intubations.