I can tell you what happened with us - our DS is now 5 months old, but he also was a very sleepy baby who did not feed much or often. He usually had to be woken for a feed, and even stripping him down to his nappy and washing him with a cold wet cloth would barely wake him when he wanted to be asleep, and then when he did feed he would fall back to sleep really quickly with the hormones, so we had to battle to keep him awake.
How large is your friend's baby? Our DS was 9lb 8oz born, and dropped continually for two weeks, to 8lb 9oz at his lowest point, and it took him until he was five weeks old to regain his birth weight. We were all concerned, and we had lots of supervision from midwives and doctors... and we were readmitted to hospital at one point so they could check his latch and basically prove that I was actually bothering to feed him!
Everyone confirmed that he had a good latch and had a good technique, and it was blatently obvious that I had a good milk supply . But by the time he was a week or so old he was having short periods awake after a feed and then he was alert, happy and interested in the world. On top of that, he was having plenty of wet nappies, with clear urine, so he wasn't dehydrated. Blood tests all came back normal, and although he was a little jaundiced, it wasn't enough to warrant any treatment other than to be sat near the window, or enough to cause the degree of sleepiness.
In the end, they just concluded that he was a happy, healthy baby who just needed a bit of time to wake up - he was probably a bit 'overgrown' in utero for his genes and so could afford to coast a bit longer than usual. Once he began feeding he settled on his adopted growth curve and has stuck rigidly to that ever since. The paed confirmed that he would be perfectly happy if that happened, and would only be further concerned if he started falling below that adopted curve or actually started to lose weight again.
I woke him religiously to feed - every 3 hours during the day, every 4 hours at night - and expressed/collected milk in a shell and cupfed (and later, bottlefed) him that milk after a feed. That seemed to be useful at first, as it was easier/needed less effort for him to take it that way, so I could get in an extra ounce or so, but it was never hugely successful - I had so much milk and it was dripping into his mouth, he just couldn't be bothered to swallow - it would just run straight back out of his mouth as he snored on . But, it showed willing, on my part, at least!
But at no point was I ever encouraged or told to give him formula, unless I chose to instead of or as well as expressing for the top-ups. In fact, I was expressly told that there would be no benefit to the baby to do that - my milk was just as good, if not better. It would have been different, I suppose, had he been taking more of the top-ups he was offered, such that I couldn't keep up the supply to meet the demand. But please, don't worry that FF will be pushed unnecessarily - IME it was not at all.
Blimey that was long. But I hope it helps.
Jen