Hi - and Welcome!
That sounds like a pretty nice starter system there! Upgraded A2000s like that give some of the best value for money in the Amiga range; they're not expensive but they're very expandable!
First, a recommendation: Get Kickstart 3.1 ROMs fitted, and upgrade to OS3.1 or OS3.9 depending on which you prefer. Personally, I run 3.9 on my A2000. Next thing is a graphics card - a Picasso II is a good basic card for an A2000.
As for your particular problem, the answer is no, you don't need a floppy disk. That set up should boot up from the hard disk just fine.
What kind of hard disk is it exactly? You say it's a Quantum 100MB - is it the Quantum 105S? That's a half-height drive (i.e. it's big!). They're good reliable workhorses but when they've not been used for a while, the lubricant in them seizes up. Check yours is actually spinning up - you'll hear it and feel it! If it's not starting, don't worry - you just need to give them a few sharp raps with your hand or something to loosen them.
Good luck! Let us know how you get on with your new toy.
