Not quite. While the all-station "Sprinter" services provide level access (if operated with SLT or FLIRT), if you want to get into an intercity train (VIRM, DDZ, ICR, ICM) you still have to step up from the platform into the train. The next generation of IC rolling stock will provide level access, but these trains won't enter service until 2021.
When it comes to accessible double decker trains, Siemens have developed a hybrid platform called "Desiro HC" (High Capacity): by combining single-deck end cars with double deck intermediate coaches, Siemens aim to optimize capacity while providing a fully accessible train. Traction equipment is located in the single-deck cars, which leaves more space for passengers in the trailing cars.
The French have taken a rather interesting approach by mixing double-deck coaches with single-deck intermediate coaches. The double-deck coaches provide a lot of capacity by just offering seats. Doors, toilets, facilities for prams and wheelchairs, and traction equipment are all located in the single deck intermediate coaches.
This is the Bombardier OMNEO, also known as the Régio2N:
Could a OMNEO like design work on the British rail network?