I've been toying with a character idea: A bard that will wander the land.

For this idea, I am considering splitting up after leaving Helgen and going my own way. My question is, Will I be able to enter Whiterun when I get there?

I ask because on all my other playthroughs, the guards stop me at the gate and don't let me in until I tell them Riverwood is in trouble. Is it possible to get into Whiterun without stopping at Riverwood and getting the quest first?

Bribe their asses.

Yes, it is possible. I'm pretty sure you'll have the same dialogue options even if you didn't stop in Riverwood. I went straight from Helgen to Riften on my current character, never having stopped in Riverwood, and I was able to later enter Whiterun as usual.

Come to think of it, one of the choices is basically, "I was at Helgen and saw a dragon! I need to tell the Jarl!"

Thanks

this. you dont need to pick up that quest at all

Yep. There's no issue getting in. Besides, the security in Whiterun is terrible.

Yea you could even kill or pickpocket to get the key to the gate from the guard lol.