No it wouldn't :|
It would make for hilarity though when Gil finally decides to unleash Enma Elish completely and Gaim regains his full power just in time to undo the dimensional rip. Gil's face after that would be all sorts of funny.
For a serious crossover:
Final Fantasy Tactics X Fate Stay Night
During Tohsaka Rin's preparation for the 5th Holy Grail War, she had been stocking up on gems for her magecraft for the better half of her life. One day, while shopping for gems, she heard a rumor of of a set of 13 crystals being auctioned. They were apparently large as stone yet beautiful as jewelry. More rumors floated around that the stones were innately magical, each having a different color and symbol of the zodiac. This piqued Rin's interest so she joined the auction just for that set of gems. She bought the set surprisingly cheap. She had her heart set on emptying her pockets the moment she saw them presented to the bidders. However, suprisingly nobody wanted them. She only had to bid against someone once and that only upped her initial offer by 10,000 yen. It was after that she learned of the dark rumors circulating about the stones being cursed as everyone who previously owned them died a gruesome macabre death as it usually entailed their entrails being scooped out.
Rin ignored those warnings ofcourse and brought the stones back to her home to experiment with her magecraft. They had turned up to be inactive with her magic and through many failures, she ended up throwing the stones into the trash in her anger. However, she had missed one stone, the one marked with the zodiac sign of Virgo.
Months pass and Tohsaka is to summon her servant. When she performs her summon, it is unwittingly in the presence of the Virgo stone. Though she uses her own gem as a catalyst, things go out of her control very quickly. Her summon sparks and sputters before a dread chill fills the room. It vanishes as quickly when a loud crash can be heard above in the attic. When Rin goes to check what happened, she is surprised to find herself faced with a blonde woman armed to the teeth with a bow, crossbow, and sword resting against noble blue clothes and thick leather armor under a metal breastplate. The woman introduces herself as the servant Archer, true name Agrias Oaks.
Rin eventually figures out that Agrias is not of their world which should be impossible because of the way the throne of heroes works. But when she is asked to recount if there had been any strange things going on, Rin tells her servant the only strange thing she had in her house was a set of fake magic stones inscribed with the zodiac. Agrias reacts violently to this and scours the room where the summoning took place until she find the Virgo stone. Agrias explains that the stone was a holy stone from her world that was pure power with a fair bit of self sentience. It would be inert to anyone it did not resonate with. However, the stone was also a gateway for demons known as Lucavi whose goal was to summon a great devil, Ultima. Agrias asks where the rest of the stones are and Rin pales as she says that she threw them out. Agrias is innerved as Lucavi can be summoned by someone with an impure enough heart and restart the preparations of summoning Ultima once again. Rin then remembers about the gruesome murders and is informed by Agrias that such bloodshed is needed for the summoning of Ultima. Double bad as now Rin realizes that demons are running around killing people to power their demon god summoning while servant are killing people to power their own mana reserves and a the same time the demon summoning.
Life was just great for Tohsaka Rin don't you think?