The fact that a T1 amp, rather than the specified T0.63 amp, fuse was used mostly suggests to me that someone found T1A fuses in a shop before they could dig up a 630ma one...
You "Can", with very big quotes around it, make use of a fuse that has a higher capacity rating [and slower trip speed] and have a device run reliably. However doing so will give up protection rating to the equipment, and possibly yourself.
Using a lower rated fuse, or one designed to trip faster than specified, is a good way to spend a lot on fuses...