The answer is no. The main sequence is a sequence in mass (and not a sequence in time).
The most massive stars are located at the the top left (since they are the brightest and hottest/bluest). The lowest mass stars are are located at the bottom left ( since they dimmer and cooler/redder).
Following the main sequence from the top left to the bottom right is thus a sequence from high to low mass.
A little bit more background
The astronomers Hertzsprung and Russel were among the first to note that the brightness and colors of stars are not just random, but that the large majority of stars show a narrow relation between brightness and color. The brightest stars are typically bluer (= hotter) and the dimmer stars are typically redder (= cooler).
When plotting the properties of stars in a diagram that shows the brightness on the vertical axis and the color (or temperature) on the horizontal axis, it turns out that the large majority of stars lie in a fairly narrow strip in this diagram. We call this stip the main sequence, simply because most stars lie on it. ( There are exceptions, for example red giants and white dwarfs do not lie on this sequence, but these are more rare). We now call this diagram the Hertzsprung-Russel diagram.
Most stars lie on this sequence because they spend about 90% of their life time there, without changing much. The sun is also one of the many stars on the main sequence. All stars on the main sequence are powered by nuclear fusion of hydrogen in their hot centers. This is such an efficient source of fuel for a star, that it lasts for 90% of its life.
Computer models helped astronomers to understand how stars move through the Hertzsprung-Russel diagram when they get older. When stars run out of hydrogen fuel in their centers they start changing and they leave the main sequence. This is when they can grow to become red giants. These changes relatively fast. This is why we do not see many stars away from the main sequence. The tracks of how stars move through the diagram as they grow older are called evolutionary tracks. These evolutionary tracks can be thought of as a sequences of time.