This can of course happen as it does in mediation and in conventional legal representation. Under the terms of the collaborative agreement, the lawyer must withdraw from acting from their client if he/she has withheld or misrepresented information intentionally or is participating in the process in bad faith. Likewise, it is open to your collaborative family lawyer to advise you to withdraw from the process if they do not consider that your partner (or indeed their lawyer) is keeping to the terms of the agreement.
If you consider that your partner is unlikely to be honest during the collaborative process, is likely to lie about his or her financial affairs, then collaborative family law is unlikely to be a good choice for you.