Is a sleep study an accurate way to determine if a child has GERD?

my daughter is 4 1/2- after frequent croup episodes -every month. and constant viral upper respiratory infections- we had a sleep study done on her.  They agreed that she has severe obstructive sleep apnea and gerd according to her study.  Is a sleep study an accurate way to diagnose gerd- i know it is the least invasive way- they prescribed Prevacid and then another sleep study after 2-3 months.  Her tonsils and adenoids are not very large according to her ear nose and throat doctor- and he said to try using the Prevacid first and see if her sleep study results have improved.  When she was a baby she cried uncontrollably for the first 3 months- and as a toddler- whenever she would wake up in the middle of the night she would scream holding her stomach, choking and having trouble catching her breath almost- also having a croup cough.  She also is very constipated at times- can constipation cause GERD? any info would help thank you.  Do you think I should see a gastroenterologist also or use the meds and redo the sleep study first?

Dina