I understand your question, but a little more information could be useful. I will try to give you some ideas. You have a slightly complicated situation here. If you are using a conventional expression vector system such as pET (you haven't stated what plasmid you are cloning in to), then the NcoI site (or NdeI site) is typically designed to contain the initiator codon and gene inserts should be amplified containing an NcoI or NdeI site tag that overlaps the start codon for the native gene you wish to express. Following cleavage of your plasmid and PCR fragment, their subsequent ligation will result in the reformation of the NcoI or NdeI site and put the ATG of your protein in a position that is compatible with the upstream ribosome binding site (RBS).

Now, it may be possible to mutate out the NcoI site in your plasmid. A simple NcoI digest, blunt ending by klenow fragment or T4 polymerase, which ever is appropriate for you, and performing a blunt-ended ligation. It should be possible for a ribosome to attach at the RBS on the mRNA transcript (transcribed from the T7 promoter) and scan along the mRNA until it reaches your ATG, but this is by no means ideal.

In answer to your first question, if you try to express the protein as it is you are going to get expression from the ATG in the NcoI site resulting in translation of a non-native protein. Assuming, as I think you say, that your ATG is in the same reading frame as the NcoI ATG, then you will end up with an extra 6 (?) amino acids on the N-terminus of your protein. If you aren't bothered by a non-native N-terminus, then go ahead and express. If you are, then see my first point. If your protein ATG is not in the same reading frame, then you may get some inefficient expression from ribosomes that read through the transcript to your start codon, but this is not certain.