Not necessarily.
My MIL is just as involved with the GCs of her son as her daughter.
I know people who love their MIL more than their mum's and so the MILs have involvment with GCs according to that relationship.
Generalisations from years of reading these threads:
Bring your boys up to be responsible for relationship management with you. Don't just expect it to be something girls (and wives) do.
Be interested in any future DIL as a person, not just a bearer of future grandchildren.
Yes, lots of women may want their mums around as birth partners, help around the time of the baby. This isn't a criticism of you - it's just they do know their mum's better. The GC will be around for years, don't spoil the relationship by getting upset in the first 2 months.
If you weren't close before the arrival of GC, don't expect to suddenly be involved now a baby is here. It's bloody rude. Don't expect the DIL to do all the running around either.
Listen to the parents. They may sound nuts compared to what you did when you were parenting but on somethings they may have a point. Watching my ILs bicker about who is most aggrieved, parents or grandparents it is 6 of one and half a dozen of the other. Yes, the grandparents are bonkers not to put out a fire-engine toy for girls to play with but neither does a bruise need to be photographed everyday. However if you annoy them, they won't trust you and then there will be no babysitting.