Tough to make sweeping statements about this.  People who don't take
good care of their health generally don't take very good care of their
teeth either, so cause and effect are somewhat hazy except in some  very
specific areas.
    Lately, there has been a lot of research connecting specifically
periodontal disease with cardiovascular and cerebrovascular disease, and
low birth weight in children of mothers with periodontal disease.
    Certainly someone with severe dental issues is more likely to have
subpar nutritional status, and chronic infection isn't going to help
overall health, even with a normal immune system.  Cold sores eruptions
specifically tend to be stress-related, so this certainly could be a factor.
    Glad to hear your brother is taking care of his teeth.  As far as the
cold, I can't say specifically--in large parts of the US the allergies
have been so bad for months that half the people I know seem to have
chronic colds.

Good luck,
Steve