Does using a free web hosting service effect the amount of traffic you get to your site?

Technically it will not, unless of course your free web hosting has a limitation of bandwidth per month. If that is the case, it will be block from access.

If practice it will as normally people don’t take it seriously when it come to free web hosting. This is especially true if you used it to sell things. Just image you go to a site at freewebhostingabcdef.com/mysitehere
Do you think you will buy it from there ?

Other than the human factor mention above, I don’t see any relation between traffic and web hosting. However if you take SEO into part of the factor, it might have some effect as well.

If the free site is like: freewebhostingabcdef.com/mysitehere
, then SEO is most likely be affected.

If it is like mysitehere.freewebhostingabcdef.com
, then should be fine