If there were no demarcation of time, in terms of BC and AD, how would it have affected the study of history?

The use of BC (or BCE) and AD (or CE) creates a fixed point of reference for events which have occurred throughout history. It is difficult to say when humans began using calendars, or even began to care about the passage of time. The Ishango Bone, a baboon's fibula etched with a series of lines, dates to about 22,000 years ago and may represent the earliest means of tracking time. It is thought to have been either a counter for the lunar cycle or a woman's menstrual cycle. Even if this is the earliest evidence of keeping track of time, it doesn't tell us much about what humans thought about the solar year.

Perhaps the biggest trouble in establishing continuity for historical reference is that it requires a fixed point to relate to. Since we don't know exactly when humans started keeping track of years, and for the fact that keeping track of the solar year may have come into fashion at different times in different places, it is difficult to determine a "year zero" for humans keeping track of time. 

Numerous calendar systems have been developed throughout history. Some marked cyclical time, like the Mayan Calendar, and others track time in a progression from a fixed beginning point. Some means of tracking time use the lifespans of rulers, as in the traditional Japanese calendar. The Gregorian or Western Calendar, which much of the world uses formally, is based on the demarcation of BCE/CE (or BC/AD) and progresses ever onward with the revolution of the Earth around the Sun.

Using BCE/CE (or BC/AD) gives us a sense of what happened before and after a fixed point in time, namely the presumed birth of Jesus of Nazareth. This way of organizing time is clearly religious in origin but is used in even secular studies, today. The greatest benefit for historians is that using the BCE/CE transition as a fixed point in time allows us to assign fixed dates to other events, people, or objects. If we were to use relative time, where one might say something occurred so many years ago, the dates for events would constantly be changing. Textbooks would have to be republished every year to keep up with the shift from x years ago to x+1 years ago. The study of history would be far more tedious if we had to speak and write in relative time, and one might never really be sure how "up to date" a piece of writing was.