I think the biggest issue here is that you're likely to find strays won't respond to commands that, for a normal dog, would work at keeping them from following (stay or wait).
I've actually had this experience as well when walking along a canal with my husband, a narrow boat owners dog followed us for a good 200 yards before we walked him back and got them to take him inside. Unfortunately with a stray, or dogs that are allowed to freely wander, there's usually no one to give them back to.
What are the implications(If there are any) when a few dogs/puppies decide to stick with you on a hike?
From the dogs point of view:
For a stray dog probably very little, most dogs have a good directional sense and can probably make it back to wherever they call home without an issue.
For an owned dog walking free probably again little - however, if the dog has tags, try and return it to its owner as it may have actually wandered off without them wanting it to.
For any puppy depending on age, probably this is the least favourable walking companion as for one, puppies don't have fully developed bones until approximately a year old, their bones are soft, and long hikes are never advised by vets until about 6 months old. They can damage their bones when they're still soft from walking too much. Also, puppies are much more susceptible to diseases like parvovirus, and other viruses which are spread by rats urine (commonly found along rivers and water sources).
From a hikers point of view:
Irritation is probably the biggest factor. You may find issues if the dogs are aggressive or there are a large number of them in a pack. If this is the case, try avoiding going near the dogs in the first place.
This answer gives great information about dealing with wild dogs, especially if they are aggressive.
How do you shoo away a stubborn dog/dogs/pup/puppies, for their own safety?
The usual way to get a dog to stop unwanted behaviour is to ignore them - this is a very powerful tool for a human as dogs want eye contact. Don't look at the dog and don't speak to it. Any form of attention to attention deprived dogs (so positive OR negative) will fulfil the need, common in owned dogs in the form of separation anxiety.
Also do not run from the dog! This is a game, you are prey, you're invoking the dogs natural want to chase. And stay calm, if you calmly walk away from the dogs they'll likely get bored. If there are locals around you can ask them to help you out, especially if the dog is known to them.
5 non violent ways to deal with stray dogs