Did the marriage between Romeo and Juliet have any effect on why they committed suicide at the end of the play?

I would say it had some effect, but was not the main factor.

It is certainly the marriage that starts everything in a downhill motion. Because he is married to Juliet, Romeo refuses to fight Tybalt, causing Mercutio to fight Tybalt instead, leading to Mercutio's death. In a rage over Mercutio's death, Romeo kills Tybalt. Because he kills Tybalt, Romeo gets banished, and because Romeo is banished, Juliet goes to Friar Lawrence, who sets his dangerous plan in motion. Friar Lawrence's plan backfires, resulting in Romeo and then Juliet's suicide. The marriage is the catalyst for this chain of events that culminates in the star-crossed lovers' suicides.

The marriage between Romeo and Juliet influences Friar Lawrence's decisions. Because he married the two, Friar Lawrence feels responsible to help Juliet feign her death and run away with Romeo. If Friar Lawrence hadn’t performed the marriage ceremony, or indeed condoned it, he probably would have advised Juliet to forget Romeo and marry Paris. Marriage is a holy contract in the eyes of God: in Act II scene VI, Friar Lawrence says, "So smile the heavens upon this holy act," referring to the holy joining of Romeo and Juliet in marriage. Therefore Friar Lawrence will not allow Juliet to tarnish the sanctity of marriage by marrying another man while her first husband is still alive.

The marriage also influences Juliet's decisions for the rest of the play. Juliet disobeys her father and refuses to marry Paris partly because she is already married to Romeo. It is illegal and immoral for a woman to be married to two men at the same time, even if one of her marriages is secret. Perhaps if Juliet was not married to Romeo, she would allow herself to eventually get over him and go through with the marriage to Paris.