I think that is entirely up to you and what you intend on studying as a part of the Middle Ages. But as a general vague response, I would say yes, up to a point.

If you want to learn everything that there is about Medieval England for example, then yes I would advise reading a series of survey history books, such as Robin Fleming's Britain After Rome for the early period and moving on to later surveys of the kingdom of England. You could then mix in other elements as you go along, for example if you want to learn abut daily life or milhist in England, it becomes a lot easier once you've narrowed the scope of your interest. It is after all much easier to learn about one specific campaign in the 100yrs War than to learn about all of Medieval England's military history.

Where it would get more complicated was if instead of a specific area of Medieval Europe, you were interested in a particular topic of theme. For example if you were more interested in medieval culinary culture, then you would want to cast a wider net, both temporally and geographically for your investigation, and it would be a good idea to read a book about one place and time and then a different one. For example moving from A Handbook of Anglo-Saxon Food and Drink by Ann Hagen to something that covered feasting culture in Burgundy in the 15th century would not tell you much about the particular histories of those areas, but would give you a sense for the changes in culinary patterns over the course of the Middle Ages.

I hope this helps!