On the contrary, if longer-term interest rates remain low, this would imply prolonged low growth, given that inflation expectations are unchanged. As a footnote, let me point out that one needs to be careful in discussing the effects on an economy of a case in which interest rates are increasing in a desirable way.
For example, in case of fiscal consolidation, if the assumed interest rate level rises, it will increase the interest burden in public finance. On the other hand, an increase in revenue can be expected from a rise in economic growth. Thus, it is important to discuss fiscal consolidation by taking account of these two effects.