You can but it is usually not the smartest move. Besides, you can make big mistakes early on that can hurt or wreck your claim.
Keep in mind the insurance company is not on your side even if it is your own company. Everyone knows insurance companies want to save money, and motorcycle lawsuits are expensive.
Sometimes, that means the insurance company will find excuses to reduce your settlement, such as claiming you contributed to your injuries by not wearing full gear, by alleging you were all or partially at fault, by holding your recorded statement against you and so on.
But most importantly, by trying to handle it yourself will just allow the adjuster an excuse to set a lower “reserve” of money on your claim. Right after your accident and well before the insurance company makes you an offer, level the playing field with the professional adjuster by first talking with a motorcycle accident lawyer you can trust. You can always go back to the adjuster, but when you do at least go back armed with knowledge.