It's not a case of being natural or unnatural, but one of a misunderstanding of the conventions. There is no such thing as 'multiple periods'. There is only ever one period/full stop. Three 'dots' is an ellipsis, meaning that something is missing, or more informally that the statement is unfinished.
In fact, the interesting thing here is that your 'line of dots' actually has the completely opposite effect of what you intended.
As the other members have explained, for a European reader, a line of dots at the end of a statement suggests an unfinished statement and trailing off of your thoughts. This can imply a vagueness and uncertainty, rather than adding emphasis. If anything, adding the line of dots de-emphasises, rather than emphasises, your thoughts.