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Can you convert between the two style types?

Yes. The division between paragraph and text styles is actually made for convenience. In reality all styles can always store all possible style attributes.

Converting a text style to a paragraph style:

You can always convert a text style to a paragraph style simply by adding paragraph attributes to it. This is possible even if the style is based on another text style because you are adding attributes, not taking them away, and this does not cause any problems in the style's dynamic inheritance tree (see below).

Converting a paragraph style to a text style:

You can also convert a paragraph style to text styles, but this is a little more difficult. If the paragraph style is based on another paragraph style you must change its parent setting to (None) or to a text style. This is necessary because of dynamic inheritance: If a style is based on a paragraph style it must inherit its parent's paragraph attributes, and this makes it impossible for it to be a text style.

See About inheritance in styles for more information on dynamic inheritance.