I once had someone ask me whether Calvin decided to push for the death of Servetus based on 1 John 5:7. Here is my answer to that question.
Servetus was executed 1553 CE in Geneva. Harold O.J. Brown (in his book "Heresies") notes that the driving impetus behind Servetus' execution was actually the imperial decree known as the Justinian Code which made it clear that heresy was a crime against the state. Although Justinian I ruled from 527-65 CE, the code bearing his name was not promulgated until a millennium later. Nevertheless, this code allowed Servetus to be executed and burned at the prosecutorial hands of Calvin. See page 186 of Brown's study.
Brown writes: "As a young man, Servetus propounded the distinctive views that ultimately led him to the stake: his On the Errors of The Trinity appeared in 1531. He held God to be one Person only; this God was the literal, natural father of Jesus Christ, who was therefore God's natural Son . . . Although Servetus denied the deity and preexistence of Christ, he too was evidently trying to grapple with Christ's overwhelming majesty; he was unable to conceive of him as a mere man, even as one adopted by God, but had to postulate a direct, natural relationship with God. Servetus was condemned to death in Geneva for his denial of the Trinity" (Brown 330).
Servetus died with the words "O Jesus, Son of the eternal God, have mercy on me," on his lips. Brown concludes that "his execution in Geneva represents a stain that Reformed Protestantism has never quite been able to efface" (330).
Now back to your original question--did 1 John 5:7 influence Calvin to have Servetus executed? I do not think that we can limit Calvin's resistance to Servetus' ideas and his subsequent prosecution of Servetus to one biblical verse. Now Erasmus' Greek New Testament (1516 CE) contained the Comma Johanneum and it may have played some part in Calvin's fury. I just do not think we can say that Calvin's actions were solely based on 1 John 5:7. I would suggest that you also read Paul Johnson's A History of Christianity. On pp. 289-290, he also discusses the Servetus case and provides some information regarding how Calvin reacted after the debacle of 1553 CE.