Here are the only two exceptions I can think of where you absolutely can't insert "を":

If the construction wasn't based on をする but とする like さっぱりする→◯さっぱりとする　☓さっぱりをする

If the construction is "merged" single character する verbs like 動｛どう｝じる／動ずる、案｛あん｝じる／案ずる、命｛めい｝じる／命ずる、失｛しっ｝する、課｛か｝する、罰｛ばっ｝する etc.

However, it's uncommon to just add を in in many cases - so the result may be awkward if it's without precedent. Basically, adding an を adds emphasis on the noun the verb comes from, rather than the action that する notes. Think of 支度をする and 支度する as "to do preparations" vs. "to prepare" - either sound fine, but 誘{ゆう}拐{かい}をする and T "to do(?) a kidnapping" vs. "to kidnap" It's not exactly like that, but I guess I'm trying to show how some cases like with 誘拐 it would sound awkward.

Also something to note is that if you're adding a "を" for instance with 掃{そう}除{じ}をする. You can't add another "を". 部屋を掃除をする you would write it as 部屋の掃除をする - however this isn't a problem if you've omitted the を. For instance with 子どもを誘拐する. Again, 子どもの誘拐をする would be grammatically "correct" but would sound extremely "off".