There are two aspects this will have impact on:
- future salary prospects within your current company
- perceived value to other potential employers
Usually there is some pool of extra salary companies hand out year-by-year in the form of small-ish percentage increases. New titles are always opportunities to negotiate pay raises beyond what these annual increases would give you, so to situate yourself better for future raises, you should drive a hard bargain to come with a new title (as there is new responsibility involved, too). On the other hand you don't want to be passed over when promotions are coming up. So there's a trade-off when chosing this route.
If your short to medium term plan is to leave/switch companies anyway, grabbing titles and certifications will put you in a better position when negotiating with potential new employers.
This may differ from country to country but I don't know of any laws that force you to disclose your exact current/last salary during an interview, so accepting a lower-than-average one for a promotion that will increase standing may be a good idea.
You have to know which direction your 'future growth' is taking, then the answer will be clear.