Yes, corporate and government bond prices will be affected significantly by interest rate changes.
To answer the question of whether it makes sense to invest in depends on whether you're willing to make a macro forecast based on a large number of factors, including what decisions you think the Fed will make in the future.
I approach the problem by admitting to myself that I cannot reliably predict where bond/equity/real-estate/etc markets will be in a few years. And I cannot accurately judge others' predictions as well.
Choose an asset allocation plan that will suit you during any period of boom or bust, and stick with it!