It will be fine, I've road bikes though monsoons without a problem. If you really REALLY need something you can get a tarp for less than $10.
Off the top of my head, per bag, covering food/shelter/tools/first air:
https://www.amazon.com/B-Air-BA-GT-8X10-BL-GTRP810-Grizzly-Waterproof/dp/B0053QUAAG/ref=mp_s_a_1_2?dchild=1&keywords=tarp+waterproof&qid=1602212906&s=instant-video&sprefix=tarp+&sr=1-2
We use a tarp under fleece: http://www.amazon.com/Grizzly-Tarps-GTRP810-Multi-Purpose-Waterproof/dp/B0053QUAAG/ref=lp_511396_1_1?s=hardware&ie=UTF8&qid=1424476404&sr=1-1
http://www.amazon.com/Multi-Purpose-Waterproof-Shelter-Tarpaulin-Grizzly/dp/B0053QUAAG/ref=sr_1_1?s=hi&ie=UTF8&qid=1354632227&sr=1-1&keywords=tarp