No. A Belize IBC may open the bank account, or even several accounts, wherever the owner wants. There is absolutely no requirement for a Belize IBC to operate a bank account in Belize.
That being said, a local bank account in the country of registration may improve the credibility and “visuals” of the offshore company. The location of the account AND the company itself in the same country would appear as most logical and would not stand out of the crowd. This would lead to a perception that the particular company is indeed a regular, local business – as opposed to an “offshore” company. The opposite is also true – a Belize IBC with an account in, say, Panama, would not seem entirely “regular” to a casual observer. Such layout would largely stand out as “offshore” and, thus, possibly suspect.