Yes. When writing a number in International Format, you write it so that callers from abroad simply dial their International Access Code (varies from country to country: 00 in most European countries, 011 in the US and Canada, and different again in many other countries) in place of the + sign, followed by ALL of the digits shown in the number.
If the caller is using a mobile telephone they can enter the + sign on the numeric keypad (it is usually either a long press or a double press on either the 0 or the * key) followed by all of the digits shown, and the mobile telephone network will sort out the correct international access.
A number in London, England would be shown as +44
20 7234 5678 as those are the only digits an international caller needs to dial after their Access Code.
A number in Rome, Italy would be shown as +39
06 444 5566 because the zero must still be dialled even when calling from outside Italy.
When showing a number in National Format, place a space between the area code and local number parts, so that it is clear which part is the area code. If the area code is optional to dial for some people, such as callers located within the same area, place the combined trunk code (if there is one) and area code within a single set of parentheses. If the area code is not optional for some callers, you can omit the parentheses.
A typical London, England number might be shown as (020) 7234 5678 and a New York, US number might appear as 212 234 5678 for example.
A number in Paris, France might be shown as 01 44 55 66 77 because the area code digits are not optional within France. However when dialled from abroad, the leading zero is dropped.
Especially dangerous: 207 234 2345. Is that a US number or a badly formatted London number?
Formats (207) 234 2345 vs. (020) 7234 2345 clarifies that; and +1 207 234 2345 vs. +44 20 7234 2345 does an even better job.
The French number would show as 01 44 55 66 77 or as +33 1 44 55 66 77.
In general you have to show the number in one or other format, or else list it twice. This is because some countries use trunk codes and others do not, and because some have area codes while others have a closed numbering plan. It's not possible to cover all calling scenarios for all options in just one format, however most mobile devices will allow a number to be entered in the full International Format and can correctly 'drop' any redundant country or area code data when making a call.
This article is also useful:
http://revk.www.me.uk/2009/09/it-is-not-44-0207-123-4567.html