I wouldn't focus on the effect of the third eye chakra on astral projection specifically. Try looking at Chakras in general.
But theoretically yes, if you look into depth about relations between the Chakras and Astral Projection.
Working on Chakra balancing to achieve Astral Projection isn't vitally necessary for the process of projecting your consciousness while sometimes unbalanced chakras can disturb the process in particular cases which isn't very likely to happen.
However the relation becomes very significant when you have difficulties with Astral Projection since at tomes Chakra blockages can affect the Astral Body in some ways.
It is said many times to people who feel buzzing while attempting to successfully project that their chakras might be either clogged or aren't all balanced as needed in order to perform several forms of magick and projections.
Basically when your chakras are not in a good condition your astral body isn't in a good condition either, which explains the buzzing and possible pain.
To see if you need to work on your Chakras try to project at first. If everything goes perfectly fine and you manage to astral project, everything is alright and there is no need to bother with this. If you feel buzzing and pain while trying to project consciousness , I recommend you to start balancing and cleansing your chakras and again, meditating regulary for it. You may find tutorials about simple chakra balancing and cleansing methods by using Google or by using any other search engines you would like to use. There, you can find various methods to easily balance your chakras and cleanse them.
That is the most accurate I could be about it, there is a subtle connection and effect between Chakras to AP but it shouldn't bother.