It's impossible to eat too much fibre. There's not enough hours in the day and you'd be feeling too full.
It's hyperbolic to say you'll be constantly on the loo. Maybe 2 or 3 times per day instead of once per day or every 2, 3, 4, 5 days for those with constipation.
What you will tend to find with a fuller fibre diet is softer stools that come out easier with no pressure required. This is as nature intended.
A lack of fibre is associated with increased risk of multiple life shortening conditions.
...And as for "What if it doesn't improve?" it's pretty much impossible for someone eating lots and lots of fibre from unprocessed plant foods high in fibre to still have constipation. Give it a try. Make tomorrow evening's meal one based on dried beans that you leave soaking tonight. They are delicious with finely chopped onion, tomato puree, tinned puree, herbs and spices.