I would guess that on average men have a stronger pelvic floor and larger bladder capacity, so a man might be urinary continent for longer provided he is prompted to go regularly throughout the day?
Incontinence has many causes. Some are mechanical (e.g. prolapse, small bladder, enlarged prostate, sluggish bowel). UTIs and other illnesses can cause temporary incontinence. With dementia, eventually people lose their sense of time so it is much harder to manage your bodily needs without someone to prompt these as part of daily routine.
The progression seems to be that people lose the awareness of sensation as the bladder fills and only realise that they need to go when the bladder is quite full. A sudden sense of bladder urgency then occurs with little time to get to the toilet and manage to undress before they have to let go.
My mum no longer has any awareness of her bladder so is completely incontinent of urine. She can be sat on the toilet by her carer, have a wee, get washed and dried, but frequently still lets go a flood of urine when she stands upright.
She also has no awareness of her bowels but will 'perform' when sat on the toilet after a meal, so at present we don't have the dirty nappy problem very often. Occasionally she is out of sorts and sad, which usually means her bowel is full, but she couldn't explain what the physical sensation is that is making her uncomfortable. It's like with a toddler. You can often tell that they need toileting by their behaviour but they haven't got the awareness of "I feel like this so what must happen next is..."
Not everyone with dementia becomes incontinent before they die. However, IMO they would have done if they had lived longer. I would say Yes it will happen in a long term progression scenario. When it will happen is extremely variable, as others have said.
My MIL has had dementia for probably as long as 15 years (maybe even longer because it takes a while before symptoms are obvious to other people). She isn't incontinent, but needs regular prompting or she will have accidents. Going to the toilet only occurs to her when she is suddenly busting to go. She either doesn't feel, or ignores, the sensation of a partly full bladder.