I'm not suite sure why you don't have time to repair or repalce them before winter.... unless you plan on DIY. A professional company should be able to come in there and install new guttters in just a few days. The trouble is, early spring is when you need gutters the most and you won't be able to get them installed then either.
But that being said... in your case, you might be right. No gutters at all might actually be better than gutters with holes that direct water to the worst location possible. Either way, most of the water is still getting to the foundation perimeter...which is what the primary purpose of the gutters. Any way to jsut patch the worst offenders? Just get some sections of cheap K style or some roll flashing and try to patch them.
Previous home - 1968 single story Ranch/Colonial, 1200sqft - 11 windows
Current home - 1925 2 story Beaux Arts Neo-classical overlooking the Mississippi River, 3200sqft - 48 Windows