WI: Bulgarian & Venetian siege of Constantinople

Imagine that the Fourth Crusade was disbanded in 1201 when the original leader Theobald III died and nobody succeed him. Venice once reached a contract with crusaders of preparing a grand fleet for transporting the latter to Egypt, but with the crusaders disbanded, nobody would pay for them. The construction of the fleet has put Venice in a financial crisis, so the doge of Venice Dandolo need to find a lot of money for solving it. Therefore, he targeted at the young Alexios, who was fleed from Byzantine and promised 200,000 silver marks for anyone who can help him to restored to the throne. In order to raise enough army, Dandolo met the Kaloyan, Tsar of Bulgaria, and persuaded him to send Bulgarian soldiers to help Alexios and divied up the remuneration.

So are the Bulgarians and Venetians able to capture Constantinople? Or if they tried and failed, do Alexios have another way to pay for them?
Kaloyan was trying in this period to consolidate his rule and obtain a royal title from the Pope in exchange for a potential conversion to catholicism. As the Pope did not endorse the Fourth Crusade and the venetian diversion to Zara and Constantinople it is unlikely that Kaloyan would risk openly associating with the venetians. Better he maintains open his options either by negociating with the Pope, or by posing as a liberator of the Romans.