Yes.
There will be some on this site who suggest otherwise but insurers are obliged to cover Third Party risks for all their policy holders provided they are not disqualified from holding or obtaining a valid driving licence.
They may not pay out for damage to your own vehicle in the event of an accident, or they may attempt to recover some of their losses if they believe your actions contributed to any damage they have had to pay for. However, this does not mean that you are uninsured and you cannot be prosecuted for that offence.
In practice that is the least of your worries if you have been charged with Excess Alcohol. It is a far more serious offence than driving without insurance. It carries a mandatory minimum disqualification of 12 months (or 3 years for a second offence within 10 years) as well as attracting a maximum sentence of six months imprisonment.