If you have some boards you could put up in front of the carpet, temporarily, even to cover a fair portion or half the space, you could quickly and easily observe what happens to the sound. Many people do dampen that front wall, but carpet is a clumsy and awkward absorber.
"If you stick carpet directly to a wall, it isn't thick enough to affect more than the very highest frequencies, thus throwing your whole room out of balance! The lows and mids will continue to bounce around as before, and only the extreme highs will be soaked, leaving you with a boxy, dull-sounding room. However, if you hang the carpet a distance from the wall, it will start to have a more beneficial effect. Providing the carpet is porous (not one with a sealed rubber backing), it can be used to cover a cheap absorbing material such as medium density Rockwool (mineral wool) slab 50 to 100 mm thick, to create an effective mid/high absorber with an attractive cosmetic finish that also prevents the mineral wool fibres from escaping."
https://www.soundonsound.com/sound-advice/q-can-use-carpet-acoustic-treatment
"If you stick carpet directly to a wall, it isn't thick enough to affect more than the very highest frequencies, thus throwing your whole room out of balance! The lows and mids will continue to bounce around as before, and only the extreme highs will be soaked, leaving you with a boxy, dull-sounding room. However, if you hang the carpet a distance from the wall, it will start to have a more beneficial effect. Providing the carpet is porous (not one with a sealed rubber backing), it can be used to cover a cheap absorbing material such as medium density Rockwool (mineral wool) slab 50 to 100 mm thick, to create an effective mid/high absorber with an attractive cosmetic finish that also prevents the mineral wool fibres from escaping."
https://www.soundonsound.com/sound-advice/q-can-use-carpet-acoustic-treatment