Let me expand on the answer provided by @Mac. There are two important concepts here that need to be unpacked, 1) endurance training when in a fasted state and 2) eating either before or during an endurance training ride.
If your goal is improved fat metabolism, endurance training in a fasted state (e.g., 8 hours without food, no eating during exercise) shows larger gains than training under a fed state (i.e., eating either before or during exercise). Eating carbohydrates at any point inhibits fat metabolism, if improving fat metabolism is your goal, then this is bad.
That said, I am also skeptical that prioritizing fat metabolism should be your training goal. See below for more details.
Background
The goal of base (endurance) training is typically to improve the metabolic efficiency and recruitment of your type 1 muscle fibres, the muscle fibres type with the greatest ability to perform endurance work. Training must be done by using slow long rides (typical heart rate zone 2). The low effort ensures most pedal force is generated by type 1 fibres and because type 1 muscle fibres generate the energy largely through fatty acid oxidation, your activity will be mostly powered by fat metabolism. If you start heading out of zone 2 (harder effort) you will recruit more of your type 2a muscle fibres and start using glycogen and blood glucose to fuel muscle contraction (note some blood glucose is used even during fat metabolism, this point is important, see the bonking section) as well as accumulate a lactate debt (your mitochondria in your muscles will no longer be able to process the lactate within, dumping lactate into your blood stream).
Endurance training in a fasted state.
A large number of studies (e.g., De Bock 2005, De Bock 2008, and Van Proeyen 2010) have show that consistent training in a fasted state (i.e., glycogen depleted state) can resulted in an increased capacity for muscles (type 1 and some evidence for type 2a) to oxidize fatty acids and as well as other health benefits (e.g., insulin response/glucose tolerance, reduced weight gain under higher energy diets) and other performance benefits (e.g., faster glycogen resynthesis see De Bock 2005).
These same fat metabolism benefits were not obtained by individuals who were well fed with carbohydrates both before and during the exercise. The fasted individuals had abstained from eating for 8 hours prior to the exercise regime and did not eat during.
Depending on the study individuals exercised between 1-2 hours at an output of about 175 W. This part is key as the studies used shorter periods than the 2+ hours for your training plan.
Fat metabolism actually requires glucose to prime the reaction. If you ride too long in the fasted state you will eventually run the risk running out of blood glucose you will feel the sensation called "hitting the wall" or "bonking." Low blood glucose levels also affects neurological functioning, you can become light headed and will have trouble focusing. Your muscle firing patterns will also deteriorate.
As such you need to be very careful if trying to do prolonged endurance training in a fasted state. The participates in the science experiments where carefully monitored during both the exercise and the recovery periods.
Eating while exercising?
This gets us to your primary question of whether or not to eat. If you are aiming to train in a fasted state, eating during exercise will also inhibit the prioritization of fat metabolism (De Bock 2008). This will be the same if you ingest carbohydrates prior to your ride.
Therefore if you want to maximize fat metabolism, exercise in zone 2 in a fasted state and don't eat carbohydrates either before or during.
Eating before exercise, but not during.
I haven't found any studies that test eating a meal before training, but riding without food (please correct me if I missed a study). I suspect when you start out your body will prioritize glycogen, the switch to fat as your stores run low. I am not clear how efficient the transition will occur or if you increase the probability of bonking. Even if your body successfully made this transition, you would still have a smaller window of prioritized fat metabolism and therefore lower gains.
General Advice / Caveats
In my opinion training in a fasted state is an advanced technique that should be done carefully and under supervision and restricted to pro/elite athletes who know their body well and can intercept when something is going wrong (e.g., deterioration of muscle firing efficiency, bonking, etc). If you insist on attempting to training in a fasted state, I suggest caring energy gels and food so that you can intervene if you start to bonk.
In terms of improving your fat metabolism, the theory is that this could help you reduce glycogen consumption during a race leaving you with more energy later in the game when decisive tactical maneuvers are often made. While I am sure this is true, I think it may be over emphasized for most amateur athletes.
You can also maintain your glycogen stores simply by regularly consuming carbohydrates during a race (see Coyle et al 1986). If you are at a Pro / Cat 1 level then better fat metabolism could give you an additional edge, but I am highly sceptical that athletes below this level will see real benefits over improved training volume and improved focus during training. Both of these will be inhibited in a fasted state.
