No,
They are not connected. The RCA started in 1935 by alumni of REITS (Yeshiva University). It expanded to take in alumni of Hebrew Theological College in Chicago.
For many years it was affiliated with the UOJCA and helped start its kashrut division.
There are members of many types of Orthodox Judaism including loads of Modern Orthodox.
Agudah is considered a Hareidi organization to the right of RCA.