If I don't enter what's considered a valid street address on the billing address for an invoice, could that cause the sales tax to not calculate?

Hello,

Yes absolutely.  The automated sales tax calculates on 2 addresses, the full billing address of the customer as it shows on the sales form and if there is no address, then it calculates off the address you have set as your company address in the settings screen.

For most accurate results (especially with local taxes) it's best to use the full zip+4 zip code for your customer when entering their billing address.