Do you guys think the Shogun is really dead?
Yes, but his entire plan before the tendoshu arriving was to fake his own death. It's entirely possible that he was bullshitting that story in the letter to Gintoki and others since he knew they wouldn't be able to keep the secret.
>his early death, at the age of 20, put an end to the short marriage. The cause of death is widely reported as heart failure due to beriberi, a disease caused by thiamine (vitamin B1) deficiency.