Does increasing the size of a sample necessarily make the sample more representative of a population

No!

Step-by-step explanation:

No!

There is a famous example of that. When Harry Truman was seeking reelection, everyone thought he would be defeated - - everyone but Harry Truman.

The poles conducted a telephone pole where they phoned people to ask who they were going to vote for. Thomas Dewey had a commanding lead from people who actually owned a phone, but many poor people didn't. Truman got in by a sound majority (303 to 189 Electorial College - - about 3 million more votes in the popular vote). So if your sample is biased in some way it is doomed not to tell the truth no matter how big it is.