The straightforward answer is NO, you CAN NOT buy a bonus while playing a deposit bonus.
While we don't have an issue with bonus buys in general during a deposit bonus, the problem arises because the cost of the bonus buy will exceed the maximum bet limit set by the deposit bonus, causing you to void the bonus by breaking that limit.
For example, many bonuses have a maximum bet limit of $10 (or even less). If you buy a bonus with a $0.20 bet, the cost of the bonus buy would be around $20. This is considered a single $20 bet, which exceeds the allowed maximum bet for the bonus. As a result, purchasing a bonus or any feature during a deposit bonus will immediately void your bonus and forfeit any remaining balance.