Basically, yes.

In her book The Bully Pulpit, Doris Kearns Goodwin goes into this discussion at some length. While more of a popular history than a strict academic source, I think it is good enough for this sort of overview.

Basically, Roosevelt was making waves as the Governor of New York championing a more "progressive style" Republican party. (I use the quotations to avoid confusion in referring to the actual progressives, of which Roosevelt was not.) He was strictly enforcing things like labor laws preventing people from living where they worked and would even go around personally doing surprise inspections of factories and checking up on policemen to fight against corruption. This was mainly while he was the New York City police commissioner, but he continued it in some extent as governor.

While he was governor, he was immensely popular with the general membership of the republican party and it was expected that he would run for president in 1904 after McKinley had served his two terms. The sort of behind the scenes political elites, or bosses, who at that time controlled huge swaths of political power because of the appointment of Senators by state legislatures (meaning that if a boss could get a number of state legislators elected, they could effectively control who get elected to Congress) did not like Roosevelt because of his insistence on fighting against their corruption end strictly enforcing the letter of the law, including upholding bans on serving liquor on Sundays. The main individual was "Boss" Platt, a man who controlled the New York Republican party and had actually gotten Roosevelt elected Governor. When Roosevelt decided that he was going to tax public service (Gas, electricity etc) Platt withdrew his support and started working against him. However Roosevelt's popularity had grown to a point where they could not simply abandon him.

This is why Platt campaigned for putting Roosevelt into the Vice Presidency during McKinley's campaign for reelection in 1900 and 1901. The Vice Presidency was a position of little publicity, dealing mainly with Congress and other behind-the-scenes issues and it was thought that after 4 years as the Vice President the public would have forgotten about Roosevelt and he would be unable to be elected President.

Roosevelt knew exactly what they were doing but was pressured by public opinion to take the job. He also did not want to be seen as turning down the honor of the Vice Presidency. He wrote several letters to his (then) friend Taft, who was service as the Governor of the Philippines at the time, Taft urged Roosevelt to take the position and use the time to prepare for a presidential run. Roosevelt eventually agreed, and upon McKinley's assassination just 6 months later, became president.