My question is, if I am to play the game 10000 epochs, store all the experiences and then train from the experiences would that have the same effect as training and while running through 10000 epochs?
No, it will not. In general, for anything other than simple environments, this will give a worse result. The trouble is during those 10,000 epochs you will have been working with your initial behaviour policy to collect experience, which will not be close to optimal. Off-policy learning adjusts for that and attempts to learn the value function of current best-guess optimal policy. However, this is not perfect, and it will learn better the closer your behaviour policy is to the target policy. An initial random policy will in many cases be too different from the target policy for learning to be effective.
There are two main causes of imperfection in off-policy learning:
Variance. The more discrepancy between behaviour and target policies there is, the higher the variance will be in the sampled values, and more samples will be required to get the same accuracy.
Sampling bias. The distribution of observed states and actions will affect function approximators such as neural networks, which reduce loss functions against an assumed population on input/output pairs. Unless adjusted somehow (and basic Q-learning in DQN does not adjust this), the population you train against will be from the behaviour policy.
Are there any advantages?
It may be faster, and result in cleaner design, to separate data gathering and learning components. If you have a distributed architecture you can dedicate some machines to generating the experience and others to analysing it. However, this still benefits from routine updates to behaviour policies used to collect experience, based on learning so far.