Clearly there is no maximum weight for a usable bike. But you only have to take a quick glance at this thread to see that a lot of TR users are willing to invest a lot in both time training, but also in their equipment.
Clearly a $10k bike is not essential, but it is very very nice. A $300 bike is likely going to be not very very nice. So, there’s some tipping point in there where your hard work on the trainer, is not directly translating into enjoyment on the road because of your equipment. That theoretical line is going to be different for everyone based on many factors. If you live in a hilly area where you’re frequently putting out a lot of effort getting over the climb, or prefer group rides that surge a lot, you’ll appreciate the reduction in weight more (from your body and your bike). If you are in an area that’s flat without a lot of accelerations, it will make a lot less difference.
If you’re in reasonable shape physically (which you probably are if you’re racing) and have been doing training for more than 6 months, then a very heavy bike may in fact be the lowest hanging fruit for improving performance. A CAAD12 105 can be had for around $1,200 and weighs just under 18 lbs. In my opinion, this is around the entry point for group rides and a bit of racing without feeling like your equipment is holding you back.