Yes, valid marriage.
So, based on an intention that can only be displayed/shown after the marriage is underway then a Tribunal would decide, due to behaviours of either spouse, whether the intention on the day was real, correctly understood etc. There is an underlying belief that a person with a good intention on the day of the wedding didn't do an about face and change their intention within the first few months of the marriage.
So, if a man finds himself in a sexless marriage, at what point and with what force of will, does he decide to separate divorce and try to obtain an annulment?
The clock is kinda ticking. It is not unlike getting your money back for a pair of shoes that go wrong. You better get back to the shop early and complain because with every week that passes and they split a little more, the shop is going to say fair wear and tear.
From your answers above it appears that a child (or I would assume a pregnancy, even if the child is lost) lessens his case for the marriage being invalid. If children are conceived there was enough sex, even if that amounted to once per year.
So let's say for the first 6 months he is super patient and very kind and loving (people tend to be) and then from month 7 to 12 he starts ratcheting up the pressure. In month 13 she has sex with him on his birthday and then it is back to her normal frigid self. He is playing a dicey game as the months and years tick by because the chances of his advocate demonstrating lack of intent to procreate go down. At some point, he has to make a decision to force it to a head and say, "have sex with me once a week or I am leaving, divorcing you and applying for an annulment", OR carry on hoping that things will magically turn around.
Not unlike working for a venture capital firm in fact. I sit in meeting all the time where we ruthlessly thrash through which firms to love and which firms to bankrupt or fire the senior management. It's all roses and hopium until the dreaded day that someone like me spells out why their sales forecast is dogshit and they are going to need to be put down. I realise that is a very cold way to look at things, but it is a REALISTIC way to look at things too, given the fact that a long marriage with one child has a much lower chance of getting an annulment than a short marriage with no children.
If the man wants a normal healthy marriage and a family in the future, then he really needs to force things to a head one way or another.