That almost happened Zhai!
Frederick I Barbarossa made an agreement with Isaac II Angelos to let his army pass through on the 3rd Crusade (1189) & to supply it at fixed prices from Greek merchants. However, the Greeks price-gouged the Germans and had them closely escorted by Byzantine troops. When a scuffle broke out, Barbarossa routed the Byzantines and captured Philippopolis & Adrianople. He then wrote to his son Henry VI to gather an Italian fleet and meet him at Constantinople, which they would take by storm. Isaac realized his army was no match for 15,000 pissed-off Germans plus Henry's fleet, and finally agreed to supply & transport them across to Asia Minor (1190).
After Barbarossa's death, Henry VI captured Isaac's daughter Irene when he took Palermo (1194). He married her to his brother Philip, Duke of Swabia & Tuscany (1195). That same year, Isaac was blinded and deposed by his brother Alexius III. Henry immediately threatened war and began assembling a German army and Italian fleet to conquer Byzantium. He planned to place Philip & Irene on the Byzantine throne and "re-unite" the two empires. Alexius in a panic offered a large annual tribute, and Henry, now embroiled in his "Erbreichplan" (Hereditary Empire Plan), accepted; the Byzantine Empire thus became his tributary and remained so until his death. He sent the army and fleet earmarked for this invasion to the Holy Land as the vanguard of the "German Crusade" (1197).
Philip, however, didnt forget, and after he succeeded Henry as King of Germany, Irene's brother Alexius IV came seeking military help against the usurper (1201). Philipp agreed, but was heavily involved in a civil war against Otto IV. So he and Alexius appealed to the Crusaders then assembling at Venice (1202), and after Philip's vassal & personal friend Boniface of Montferrat took over leadership of the 4th Crusade, it was diverted to Constantinople to regain the throne for Alexius IV.
So the 4th Crusade was in a way the culmination of Barbarossa's original plan. When I get CK, that German army and Italian fleet (Venice, Genoa, Pisa, Sicily) will set sail long before 1204...