Do Adventists believe that people must obey the Ten Commandments in order to be saved?

No. Salvation is by grace alone. There is only one way to salvation. That is faith in the atoning death of Jesus Christ. No one can "work his way" into the kingdom of God. No degree of obedience, no works of penance, no amount of money entitles anyone to any divine favor. Nevertheless, "faith without works is dead." Keeping the commandments is the result, the evidence, of salvation. It is a matter of love, not legal duty. "If you love me, said Jesus, "keep my commandments" (John 14:15).

Quoted from Arthur S. Maxwell in A Handbook of Denominations

My Commitment

#2 I accept the death of Jesus Christ on Calvary as the atoning sacrifice for my sins and believe that through faith in His shed blood I am saved from sin and its penalty.

#3 I renounce the world and its sinful ways, and have accepted Jesus Christ as my personal Savior believing that God, for Christ's sake, has forgiven my sins and given me a new heart.

Official Seventh-day Adventist baptismal commitment statement