A fire science degree would help more at the company officer level, particularly at or around the BC level. As a basic FF, getting your FF1 and 2 from an accredited institution would be of much more benefit. If you need more on building construction or maybe fire protection systems, you could attend a conference to get that. You could also buy the text that the class uses, since fire sicence online degrees are popular. You're not paying for the credits, but you're still getting the same education.
Some volunteer depts do the right thing by sending their probies to an accredited fire academy. Others just give OJT tailored to their first due. They may not train you in truck work, VES, RIT, high rises, etc. At my employer, we regularly drill suppresion and EMS in house in accordance with our monthly training matrix. One month may mandate company evolutions for RIT and ropes/knots, a live burn or maze training, as well as powerpoints for garden apartment tactics, a LODD/close call, and hydraulics. EMS may be a drill with Fairfax One, our PD medevac, powerpoints on heat emergencies, COPD and asthma, as well as our quarterly continuing ed at our EMS training center, run by PA's, an RT and an RN. The common misconception with the fire service is that we sit around all day, eat, nap, and play X-Box. As you can see, we have that training I listed, along with daily equipment checks, housework, public education, requests to attend social functions such as block parties and church gatherings, collection and participation for various charities such as Fill The Boot, a smoke alarm initiative, mandatory PT, building walkthroughs and preplans, and calls, of course. The first 12 hours or so are actually quite busy. If your volly house is slow, there ought to be drilling and such.
If you're getting even half of this volume of training on a monthly basis, I feel that the fire science degree is unnecessary. Regarding career development in the fire service, degrees either help with or are mandatory for promotions, depending on where you work. It can be any degree, so you're already set. For the DC or AC level, a degree in Pub Admin, Emergency Management, or Business Admin would likely set you apart from other prospects.
Edit: For further knowledge, I recommend Francis Brannagan's book on building construction, Truck Company operations by John Mittendorf, and FDNY's forcible entry manual if you know where to get it.