Might not be the best move, but test it
Yes, multigrade is sensitive to some degree of the red wavelengths.
Test the situation. In the DARK, flash some paper under the enlarger, til you can fiigure how much light it takes to get a barely disernable grey with no multgrade filter in the enlarger ( contrast will be about 2.5 with no filter on most brands). Put a sheet under the enlarger set to say project a 11x14 image size at f16, and set the timer to something like 4 seconds. Cover all but 1" of say an 8x10" paper with a mask - like a piece of cardboard. Expose, then uncover another inch, without moving the photo paper, expose again, etc. When the sheet is entirely uncovered, then move (again in the dark) to the developer tray, and toss it in for a couple of minutes before turning your 'safelight' on. It may take a few tries to find out how long it takes to flash to the first shade of grey. Evaluate when dry under a white light source, not the safelight while the print is in the developer.
Then flash a whole piece of photo paper at once for the just before flashed to lightest grey exposure time. Put a series of coins on the paper, after it ahs been exposed and turn on your 'safelight'. Take the coins off at 30 second intervals until you make it to 5 minutes. It helps in this test to circle the coins and write the times on the face of the photo sheet with a sharpie marker. Process the paper, again in the dark for a few minutes, then pop it into the fixer for a minute before turning on the lights. You now should know how long you have before your 'safelight' starts to affect your particular paper that you use.
If it is a resin coated B&W paper (the easiest by far to start with, and you might never move to fibre), then you likely can get it fully developed in a bit more than 2 minutes unless the developer is freezing cold, pop it in the stop for a half a minute and have it in a rapid fixer for a minute and no longer substantially light sensitive.
If you do run into trouble earlier than that, then get out some black paper, cardboard and mask, turn out some tubes, etc. to cut the amount of light this 'safelight' system puts out until you can lay you hands on an OC safelight filter and safelight.
But print for heavens sake. I still can remember the thrill of printing in my darked out bedroom with an old enlarger borrowed from high school over christmas vacation one winter over 24 years ago now. I had the enlarger of a fold up card table, and processed in trays laying on top of a piece of plywood and a big piece of plastic on top of my bed. A kodak bullet safelight sitting on the same card table was bounced of the back wall and roof of the room. And man did I print, and have fun.
Within the year I had my own corner of the basement darkroom with a home made plywood sink that I still use. By the last two years of uni I was in an old house that had a second floor kitchen from before six of us rented the house whole. From there i put out the engineering society yearbook photos.
There have been three other darkrooms since then, til my present one. Even if no one else likes what you do, keep at it, because it can be a whole lot of fun, and if you keep notes, you will get better with time. My first prints from that first darkroom look like not so great today ( washing in the toilet tank was probably part of the problem), but they still feel great to me.