No. Railcard discounts are available throughout Britain but they are not available on tickets for morning peak period services for journeys wholly within London & South East Network Railcard area on Mondays to Fridays. (The exceptions to this discounted fare rule are when you travel at weekends and on Public Holidays).
The times of morning off-peak services do vary by route and are normally related to the availability of Off Peak Day tickets. It's best to check with ticket office staff before buying your tickets.