The answer to your question as to the danger of taping the lips, it is if you use a nasal mask, and tape your lips also. Nasal masks don't have anti asphyxia valve as full face mask do. So if the CPAP machine stops working for any reason then you don't have breathing air coming thru your nose and you also can't use your mouth to breathe. So essentially you get asphyxiated. If you use a chinstrap instead then it leaves some gap for emergency breathing.
Are you asking your question b/c you want to prevent a Dry Mouth?
Taping your lips don't stop air from entering your mouth from the nose and throat, i.e. from the "back side" (pharynx). When you swallow your saliva which is generated in the salivary glands around the mouth, and then secreted into the mouth and subsequently you swallow it (also during sleep), air must come in from the back to replace the swallowed saliva's volume because your lips are taped closed and air can't come in from the front to do it. So this air circulation, from the "back side", will dry your mouth in spite of taping it. It could be to a lesser degree than from an untaped mouth also b/c the air from the pharynx is moister. But, it is clear that taping your mouth to prevent a Dry Mouth, completely, is not possible.
You better off with a Chinstrap which would prevent opening the mouth very wide but would allow some lips opening to let air be breathed from the front. However, using a Chinstrap instead of a full face mask would cause the XPAP's treatment to be affected.
I myself use a traditional nasal mask with the addition of a chinstrap. I am using quite a stiff chinstrap but even if it does engage the teeth, I can still open my lips without opening the teeth. So some air does go in and out there which causes me to have a semi Dry Mouth. Especially, up at my upper front teeth. So when I go to the bathroom to urinate I also rinse my mouth with faucet water. Overall, it's not too bad. The CPAP that I am using is robust enough to deal with some mouth leak without compromising its diagnostic ability.
You can see in my recent one year report that my unintentional Leaks (which include mouth leak) were way below the allowed value of 24 Liter per Minute. During 95% of the time my unintentional rate was below 8.4 L/Min:

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