In short, no. You should only sell products if the notification has been approved and, importantly, appears on the notified products list. This process can take several months.
If a manufacturer or supplier says they are approved for sale but their product does not appear on the MHRA’s website, ask them to confirm it has been published and to provide details which show its confirmed status.
One helpful resource to use when checking if a product has MHRA approval is VapeClick – which provides access to the all MHRA E-cig ‘submitted and notified’ vape/e-cigarette data.