Is 起草 a separable verb?
Yes, in the dictionary《现代汉语词典》, separable words (离合词) are indicated with the symbol "//" in their pinyin, and 起草 is indicated as qǐ//cǎo.
起草 is a verb+object separable word.
Anyway, there is an exception to the following general rule:
Verb+object separable words cannot be followed by an object.
The following sentence is wrong:
很多事情: object not allowed
A few verb+object separable words as 起草 can be followed by an object. They are still verb+object separable words, and all other rules still apply, so we would still say "起了草", "起过草", "起的草", "起完草", "草都没起", "起一起草", "起什么草", etc. But, we can also say:
一个文件: object (normally not allowed)
Some other exceptions are:
操心, 成交, 出口, 出席, 担心, 发愁, 放心, 进口, 列席, 留神, 留心, 留意, 缺席, 告別, 在意, 注意, 走私.
For more info see 品诗文网