It depends how you do it. Generally the link between offering formula and struggling with BF is more to do with the parents' attitudes and fears than the milk feedback cycle itself.
If you offer bottles in a controlled way, increase the amount slowly and don't allow this to cross over with breastfeeding but have it as a separate thing it is unlikely to affect breastfeeding. Likewise if you mostly breastfeed but give a bottle casually/sporadically, not on any timescale, but just when you feel you want a break and this is about twice a week or less, the bottle is unlikely to affect supply. The pattern here is that breastfeeding remains the main method of feeding and the parents retain confidence in the efficacy of breastfeeding and expect that it will continue to work.
However if you give formula because you're anxious about supply, the patterns of usage tend to be different and here we see that introduction of formula tends to harm breastfeeding. This could be on the advice of a health care professional, family and friends or simply her own instinct that her baby isn't getting enough and so formula can help fill the gap. It can - but that's another story, anyway, the problem (typically) with introducing formula on this basis is that parents tend to supplement more at times when they feel breastfeeding is especially struggling, which is exactly the time when you need to breastfeed more. This creates two cycles - one where the breasts are mistakenly "given time to refill", which makes your body "think" it needs less milk and so will produce less, and one where the baby is frustrated by a slow or poor flow of milk in comparison to a bottle, plus learns that it is easier to obtain milk from a bottle and so may reject the breast, particularly if the breast is more difficult for him to get milk out of, due to low supply or transfer/latch issues.
Note that I mentioned formula top ups can help fill a gap where low supply or poor milk transfer is suspected. This can be especially helpful to give mum some "breathing space" when she is feeling anxious, is in pain, urgently needs to sleep, or in an infant whose blood sugar levels are causing concern. Best practice here would be to do this on a temporary basis and at the same time introduce a plan for increasing the mother's supply/addressing latch issues, e.g. dividing a tongue tie, and eventually reducing and/or weaning off the top ups, however this kind of follow up rarely happens in reality - parents are advised to top up and then... nothing. That solves the problem, if they are lucky, because the top up + breastfeeding combination works in itself and is either kept or is replaced with solids when weaning, some parents are more proactive and end up phasing out the top ups more quickly, either by pestering the HCP for follow up or seeking independent advice, but the majority once top ups are introduced slowly find that breastfeeding comes to an end. This is put down to the supply issues or latch issues which led to top ups being necessary in the first place. Baby is still fed, parents are happy (perhaps disappointed but generally satisfied) and so from the HCP's perspective the problem has gone away, and in reality in the current climate they are probably far too busy to follow up and check whether things are going well or whether the parents/mother would like to develop a plan for phasing out top ups.
In summary if you want to give a bottle because you just want to, do it in a controlled way as a separate thing from BF or just occasionally, and you should be fine. If you find yourself wanting to give a bottle because you're worried about feeding, it's fine to do this if it will alleviate stress or anxiety for you but also SEEK HELP ASAP, in order to get breastfeeding back on track, otherwise you run the risk of this pattern where formula undermines breastfeeding.