No, a single day of usage should not cause significant problems. It's very unlikely that it will cause a noticeable different in how your Methadone dose works. This is only one day. Things get exponentially more tricky as you use for 2-3 days. Given the potency of the Opioids out on the street right now, I could see 3 days of usage leading to a palpable decrease in the effectiveness of your Methadone dosage. At any rate, if this did happen, it would likely just mean 3-5 days of feeling out of whack before you return to your previous state of tolerance.
I highly advise against dallying with this stuff on your own free will man. If you're taking Methadone and you feel it's helping you, it's not worth it. You know as well as I do; if you can do something once, you can do it a million times. Lots of people decide they're going to use street Opioids for a single day. Lots of people say they're only going to smoke Crack once or twice.
I know I'm gonna sound like a DARE officer here. I had a friend who was in 12-Step stuff with me. She had been panhandling and occasionally prostituting to get money for Opioids. Years ago, she got on Methadone and in the process, got her kids back, got her husband back and led a pretty much fairy-tale existence considering what she had been doing.
She had a bad day or whatever and ended up using Fentanyl. When she had originally gotten into recovery, Fentanyl had not yet come on the scene heavily. Fast forward til now and she's been using Fentanyl every day, is homeless, has a restraining order from both her daughrer and her ex-husband. During this time, she got knocked up by a fellow street addict. The baby was born severely premature. She had been taking ~300mg Methadone per day and using as much Fentanyl as she could get. Imagine that baby's withdrawal as their first experience out of the womb. I'm no doctor, but you cannot convince me that this doesn't lead to long-term effects of some kind on the child.
The ups, downs and misery that is the process of becoming addicted to and dependent upon Heroin is amplified and accelerated when a person uses Fentanyl.