IF prices of imported goods increase because of an increase in
transport costs whhich takes the form of surcharges or fees imposed by
carriers on shippers and then passed on by shippers to the end
consumers, will it result in an economy-wide inflation? would this
qualify as a cost-push inflation? what could be other conquences at the
macroeconomic level of this prices increase?

Coco,
just a free comment, not an "answer" to your question.
I don't think it is that simple.  
First, the relative volume of imports to total economy will be
important.  If imports are a small part, their increased costs won't
have much effect.
Second, if the imports are competing with domestic products (in the
US, autos, for example), the producers may have to bear the increased
transport costs, reducing their profit margins, in order to maintain
sales.

I would say yes, it would lead to inflation.

Let's say before the increased shipping costs that it was a toss up
whether I would buy a Honda or a Chevy.  Then the shippers start
charging Honda $5,000 extra per car to get it to the US...  The
shippers would then offer me $5,000 to buy a Honda.

With this $5,000 incentive, Honda could (and would) charge $5,000 more
for the car and it would be the exact same deal to me as it would have
been before the increased shipping ordeal.

Notice that Chevy's did not change in price.  So the inflation would
be localized to imports...  but imports are calculated into the CPI so
there would be some effect on inflation, and the size of that effect
would be dependent on the quantity of goods being imported.