I will answer this with a categorical "yes it is most definitely possible", from my experience at least.
two close family members. Both later diagnosed with personality disorders
the first one fooled her psych for 2 years, it was only when her husband intervened and ...long story short, but more or less gave the ultimatum,
"I come with you to your therapy for one or two sessions, I tell the therapist how things at home really are, you get help for your real issues, OR, you carry on the charade you have been playing with your psych for the last 2 years and I leave you and we divorce".
second family member was similar, but they only managed to keep up the charade with their psychotherapist for 6 months as their spouse got fed up of the suicide risks and ultra-risky behaviours and contacted the mh crisis team after another suicide threat. Turned out later that the 20 odd sessions they had had in the 6 months leading up to the crisis, my family member had just been saying more or less anything that they thought the therapist wanted to hear, or would get the therapist to say "well that's you much better now, as far as I am concerned our sessions can cease". They had told maybe 10% of what was really wrong with them, 10% of the problems they were actually experiencing. The psychotherapist wasn't the kind that even tried to scratch beneath surface, so it was very easy for them to lie and be believed.
In the first instance I blame my family member, they are good at lying and could easily pool the wool over the eyes of any professional.
In the second instance, although ultimately the blame has to be placed with my family member for being every economical with the truth, I actually blame their psychotherapist too, as I feel she was WAY too willing to believe her client and disregard their spouses version of events as being over-worried about nothing.