To a lot of people, no. Any rope will technically work for a rope halter. Heck, you could make one out of wire - but there are obvious reasons why you wouldn't want to do that. It all comes down to personal choice in the quality you're willing to accept. For me, I really like the rope I use. I can get it in soft, medium, or really stiff for training halters, and I can get it in almost any color. It'll outlast most other types of rope out there, and it's polyester so it won't cause rubs as easily as nylon. It doesn't fade in the sun and keeps it strength, which can't be said for many other types of rope.
So, when it comes down to it, the rope you're probably using is fine, especially if you don't intend on selling them. However, I'd rather invest in an American-made, high quality rope.
The down side to this is I can't buy the $9 halter/lead combos anymore. They're crap. And now that I know what is good quality, what makes it good quality, and why I should want good quality, I can't bring myself to buy crap anymore. I'm glad I make my own tack, because I couldn't afford to pay what I charge as retail right now. For instance...
It costs me $8.80 to make a simple rope halter, just in rope alone. Add on what I have to pay for shipping and the special tools and supplies I bought to finish the ends for a quality retail product, and I'd be losing money if I sold my halters for anything less than $11-12. Add in the time I take to order all this, perfect my technique, and then actually make the halter and market it, and you can see why high-quality halters sell for $20-30. I price my basic halters at $23. So, for me, it's much cheaper to invest the time to tie my $11-12 halter than pay for the quality that I would want now that I know better than to buy the cheap stuff. (by the way, in costs alone, it's $22 for an 8' lead rope - so again, I'm glad I'm paying the at-cost price rather than retail, because they sell for $40)