Depends entirely on how well the immune system is building up. My personal opinion that I've no evidence whatsoever is that diet plays a main part in it.
I was rather ocd about dd's diet when she first started on solids. I put in there spinach and all kinds of goodies and she gobbled them up. She hasn't been a fussy kid and eats what we eats, which is heaps of fresh fruit & veg. She's not too big on red meat but will eat it if its mince or in a casserol, or if it's chicken or fish. She has always been a good weight, good colour to her skin (in reference to iron intake), plenty of energy and I'm also conscious of low GI foods to give her proper fuel throughout the day.
Being tired and run down from lack of energy & poor diet will mean a childs immunity will suffer. Early to bed is a big one. DD has always been in bed no later than 8pm and is up at 7 on weekdays, 8.30ish on weekends. Bubs is in bed by 7pm.
My dd went to childcare once a week for 3 hours from when she was 5 months old. Everybody told me that she would get sick and get colds one on top of the other for an entire year because of childcare, and this never happened.
I'm hoping to do the same with ds. Fingers crossed that he is also not a fussy eater.
I also believe in starting solids no earlier than 6 months, but that's another debate. wink DD had tastes of solids from 6 months but didn't want it so she didn't properly start solids til 12 months, she was a boob juice fan only.