As a bonus the fuel flow will reduce as well.
- no. Once you drag your arse in those extra miles at the lower level it goes up!
Whilst 'holding' is reasonably fuel efficient, it does take place (normally) at lower levels, therefore reducing towards endurance speed at cruise altitude is always preferable in fuel terms (and gives you longer to finish brekkie).
The only 'variable' is that with a 'seasoned eye' you might judge that the EATs will suddenly dissipate in which case being in the hold rather than toddling towards it is the best place to be.