Wondering about the viability of a Hardware Wallet
I want to roll my own hardware wallet using a USB stick.


An ordinary USB stick cannot be made into a hardware wallet. 

Hardware wallet incorporates cryptographic hardware designed for cryptocurrencies and has firmware to interact with software on another device (PC, phone, etc)


No and Yes. 

Normal wallet software has some utility while it is synchronising, but until it has synchronised it can't show the amount you control and therefore may not be able to create transactions using those amounts.

An  SPV wallet doesn't need to download the blockchain but is less secure.
A full-node wallet cannot create transactions involving unspent transaction amounts it does not know about.
A wallet must be online to send transactions.
A wallet need not be online for money to be transferred to your control but the wallet won't know about it until it is made online or is able to communicate with other software that is online.