Well I would say that
IF it shares the SAME IP address of a site that has been penalized by Google in some way then it could indeed effect your site using that same IP address too.
There is a lot of controversy out there surrounding this subject with some people saying no it doesn't matter at all as Google sees all domains differently regardless of their IP address.
And there are a lot of people who will say yes it can be effected if it shares the same IP address of a site that has been Google penalized.
Personally I side with these people because I've come across loads of people that have had their site effected due to one bad site in their neighbourhood (IP).
In the same way as one bad apple can upset the whole apple cart.
That is why you should always do your due diligence (homework) first and check out the other sites on that shared server and see if any of those sites are penalized in anyway or if they are shady sites doing shady practices if you are considering any such shared hosting plan.
How to know which sites are using the same IP address of your shared server?
Well you can use CMD command to find out or you can use an online whois tool.
First you need to find and know what your websites IP address is.
You can do that with a CMD command window using tracert
www.yourdomain.com
Or if you already have it and want to know which other sites share that same IP address you can use a "Domain Neighbors" tool.
Some such free tools are
dnsqueries.com/en/ip_neighbors.php
ipneighbour.com
majestic.com/reports/neighbourhood-checker
However... Chances are as a shared host, it will have literally hundreds and hundreds of sites using that same IP address so to check them all is not really practical and would take a very long time and a lot of work.
That is why for this reason, for a professional site, shared hosting is not a good choice.
Better to pay a little extra more and get a dedicated IP at least.
