Yep it certainly does happen!! At 5 weeks I had no hope of doing my pants up. Everyone said I was just bloated but it never went down - only got bigger. By 10 weeks I was in maternity clothes!! Did feel a little funny buying that kind of stuff so early but I was so uncomfortable in anything else.
Looking back at photos it's obvious I was pregnant. It does make it hard if you're trying to keep it secret though. Keep wearing loose things - at least you can get away with lots of layers in winter!!