You can not store AC in a capacitor so no, even if you could find a 1.1F/450VAC rated one it wouldn't work. Just for reference, the one you show is 1.5uF, that is almost 700,000 times too small !
Is the AC voltage present all the time, even when he switch is turned off? If it is, the solution is an electronic switch with a built in delay before it turns off. You can buy them 'off the shelf', they are commonly used in entrace hallways so the light stays on for long enough for someone to find a door or climb stairs before automatically turn the light off to keep costs down. They work with any kind of light bulb.
Brian.