Yes, you can get insurance with Carole Nash if you have a 'daytime MOT'. You must have a valid MOT certificate and as long as you do not breach the daylight/visibility restriction of the VT32 advisory note you will be covered.
This is true of all bikes include vintage and classic machines and off road bikes (which satisfy Department of Transport road laws and construction and use regulations).
You must ensure you satisfy any other legal obligations about the use and ownership of your bike, and take all reasonable steps to keep your vehicle in a safe and roadworthy condition.
If your bike was manufactured with lights and you remove them, some insurers may treat this as a modification and it could affect your premium. This is particularly relevant for modern and off-road bikes that have been adapted for road use.
More information:
Find the MOT inspection manual: motorcycles on the Gov.uk website.