Garp would smack Doflamingo and his entire crew alone.
One Admiral would beat the remaining Shichibukai(except Mihawk)
Two Admirals would beat Mihawk without much problems.
Sengoku would not even need to step in.
In the end you would had Garp, all admirals looking pretty clean while all Shichibukai would be dead/defeated.
I don´t even count the 20+ viceadmirals+100000 soldiers and Pacifista and other ranks.
We saw Kuma/Jinbe/Crocodile vs Akainu, they couldn´t handle him and would die if no one helped them out.
In fact Akainu would kill all the remaining Shichibukai faster enough to join Kizaru and Kuzan to face Mihawk, who would be defeated easily if all 3 Admirals helped each other to kill him.
Garp would beat Doflamingo and his crew low diff at worst...
Anyone who thinks the navy is equal to 7 Shichibukai, lost his mind.