Is it possible to calculate how many SMS messages a multipart message will take?

Yes, this is possible.

Use the following formula to approximate the number of parts before sending:

For text messages:

Number of messages = ( Number of Characters / 153 ) + 1

For unicode messages:

Number of messages = ( Number of Characters / 67 ) + 1

For data messages:

Number of message = ( Number of Bytes / 134 ) + 1