Do any of the upgrades (bathroom, treadmill, pool, etc) improve a peep's health? If I add these upgrades will they keep my peeps from getting sick and therefore the related Trophies to healing?

I've advanced my first (but not initial) family pretty quick. So far I've upgraded both the office and workshop to second level and the kitchen to third and I've purchased all house upgrades except for the ones which I think relates to improving health (see above). I just don't want to miss out on any of the Trophies. Maybe I'm a completest.

Thanks!