There will be a coronation, but if the monarch succeeds before adolescence, it will be delayed until he is adolescent. The Russian example I can think of is Peter II, who was 14 when he died just before his coronation. The last English monarch to succeed under age was Edward VI, who was nine. He was certainly crowned before he died at 15. Edward V, aged 12, was about to be crowned when he was deposed (his uncle, Richard III, was crowned instead). Henry VI, who succeeded at nine months, was crowned at ten.
So, if Mikhail had succeeded Alexander III in 1894, he would quite realistically have been crowned once official mourning was over. If Alexei had succeeded in 1917, then they might realistically have waited a couple of years for a coronation, but not necessarily until he was adult.
Ann