Short answers: No - if the issue is handled correctly. Yes - if the issue is handled incorrectly.
Proper goal setting with your child is essential. If parents express their children's self-care goal as "keeping yourself healthy" or "making sure you don't become ill or have a regression," they set their children up for failure when dealing with many diseases that often run a progressively more threatening course.
Then, as the questioner notes, if the illness progresses, the children may feel like a failure when they have been taking good care of their medical problem. Even if the parents have been taking the primary responsibility for care, the situation can still work out poorly. The children may feel guilty about disappointing their parent, blame the parent or they may hide their symptoms. Either way it's a lose-lose situation.
I've also noticed that, during occasional resistance to treatments, I might (unthinkingly) say something to the kids like, "If you don't do your breathing treatments, you'll get sick." It comes from the "parental lecture lobe" of our brains and is similar to the "If you don't wear your coat, you'll get sick" lecture that comes squirting out of our mouths so naturally. This can also cause our kids to feel like it's their fault when they get sick. A better approach would be to use choices and/or enforceable statements to handle power struggles and resistance rather than lecturing or threatening.
Hostile-dependency is a major issue when dealing with a child's medical issues who tend to get spoiled because of the many problems they face. Hostile-dependent children are entitled and demanding. There is a metaphor: "That child bites the hand that feeds him." They may also be referred to as "spoiled rotten." Such children put parents (and others) in the position of feeling obligated to do things for them that might be freely offered to respectful children.
This unfortunate cycle starts with parents not setting their own self-care boundaries. See the cycle illustrated on page 205 in the book Parenting Children with Health Issues (also shown in the Powerpoint Presentation on this website).
Step 2: Make an observation: "It makes me feel sad for you when I see you (hear you) ______.
Step 4: Wait with patience and anticipation (but try not to show glee) for a point within the next few days or so when your child will want something that would take energy to provide and is medically safe to withhold. This could be either an action (cooking a big dinner, taking the child some place he or she wants to go) or a material offering (something that you would usually pay for or provide).
Saying "unhappy" at this point is probably an understatement because entitled children pitch memorable fits and historically remarkable tantrums when they don't get their way. The secret to success is to remain empathetic, calm, (not reassuring, pleading or showing frustration) and stick to your guns. Unwise parents get noisier, show frustration, and finally become angry.
There are examples of using the Energy Drain Technique for medical issues on page 62 in Parenting Children with Health Issues and in other Love and Logic publications for general parenting issues.
Of course they immediately say (ever so sweetly), "May I please have ___?" to which we calmly reply, "Nice try. Next time, ask just like that- the first time." They generally respond with something like, "Aww, man!" and that's the end of it.