The simple answer to this is clearly "yes, they could". It appears that the glide path could be made steeper through the use of flaps alone. I'm not clear what the benefits of using speed brakes (or even landing gear) instead might be.
I didn't ask about the fuel consumption questions. However, contrary to what is argued by Bianfable and the apparent biases of most of the commenters who have responded to this question, the issue of fuel consumption does not appear open and shut.
An interesting paper at Research Gate, entitled "On the Influences of an Increased ILS Glide Slope on Noise Impact Fuel Consumption and Landing Approach Operation" concludes as follows:
Steeper landing approaches can lead to a significant noise and fuel reduction. Having regard to the sink rate limit of 1.000 ft/min below 1.000 ft height they can be performed only up to 4.0° glide slope angle. In addition a change of gear/flaps schedule is necessary to fly approach angles of more or equal 3.5°, which can reduce the noise benefit gained from the higher flight path.
Note the use of the word "significant".
Note also that this paper is concerned primarily with the whole final approach glide path (i.e. until touchdown).