Let’s cut straight to the chase. No, you cannot use an Adventure as your Signature Spell.
Throne of Eldraine introduced a new subtype of instants and sorceries: Adventure. This mechanic is embedded within a creature card. The Adventure has it’s own mana cost, name, type, and rules text– but the card that the Adventure is on is a creature card.
When you cast the card, you choose which part you are casting. If you cast the creature, the card goes on the stack as a creature spell. It can be countered or responded to. If it resolves, it enters the battlefield as a creature.
If you chose to cast the Adventure, it goes on the stack as an instant or sorcery. It can be countered or responded to. If it resolves, you follow the instructions of the spell and then put the Adventure into your exile zone instead of your graveyard.
If an exiled card you own is on an adventure, you may cast the card as a creature spell from the exile zone.
For example, Lovestruck Beast [] is a creature card filled with Beauty. When you cast it from your hand, you get to choose if you are casting lovestruck Beast [] or Heart’s Desire. As a result of that choice, the card goes on the stack as either a creature or sorcery. If you cast it as Lovestruck Beast, it will enter the battlefield as a 5/5 creature when it resolves. If you cast it as Heart’s Desire, it will create a 1/1 Human and then head into the exile zone. It will remain there until you decide to cast the Beast from the exile zone (or until your opponent casts a card like Memory Theft [].
While this is a fun and crazy mechanic, the card itself is a creature card; the creature card, even though it has an Adventure, cannot be used as a Signature Spell.
Level 3 Magic Judge, Keeper of Bad Jokes.