He was able to force Mary to join in his war against France, despite the disastrous consequences for England. To be honest, Philip himself was very unhappy with the marriage terms that were listed above, as they were brokered by Parliament. Even men like Gardinier didn't want Mary to marry him, and there really was not precedent for a female ruler in England yet. Hence the strict articles imposed. Otherwise Philip might consider himself a jure uxoris king and lay claim to England by right of the crown matrimonial (not that would've ever gotten it - Parliament already had great control in regulating the succession). He took the marriage up only for political purposes and for perseving the Low Countries. There wasn't much he could do about those terms, but essentially he was meant to co-reign with her. There was one particular demand that English laws had to be printed in Latin of Spanish as well, because Philip couldn't read English; it became treasonable to deny his royal authority in Ireland and England. There's a neat difference in the Great Seal before and after her marriage: before her marriage, Mary is seated alone, the crown on her head. After, she seated in a deferential position to Philip, although the crown is between them and hence "shared."
He definitely played a part in the statescraft of Mary's reign--when he was there. He was the one who persuaded Parliament to the repeal Henry's religious laws (The Second Statute of Repeal). Before that, Mary's first statute had merely nullified Edward's religious laws. Another issue is his distaste for Mary meant that he spent most of his marriage abroad (IIRC, he was only in England for around 1554-1555 and 1557 for a time. Philip was even partially against Mary's burnings of so many heretics, and his advisor Simon Renard warned him that, "such cruel practices would cause a revolt," and inflame anti-Spanish and anti-Catholic sentiment.
In short, Philip definitely had vested or shared powers with Mary... but he was only in England for barely two years of their entire marriage. He helped get the Second Statute Appeal through Parliament in 1555, and then in 1557 convinced Mary to join his war against France. I think he used his authority definitely only when it benefited him, and his own domains.
Hence why I think if they had a child and Mary Tudor died on time, Philip would be Regent but in name only, and we'd have an actual Lord Protector who would have actual authority to rule in the young king's name.