In HTML5/JavaScript you can get input from user and display pictures. Just like in many other programming languages. And your are already on the internet, so internet stuff should be easy too. Which is all you need to make a game.
The problem is not what is possible and what is not, because in theory anything is possible, but whether trying many things together would be still fast enough. Which depends: on computer speed, on computer, on browser speed, perhaps even on internet connection speed. And all these data change from player to player, from year to year.
So you could start with an analysis: what do you want your game to be able to do, when the screen is most full? For example, to display 50 monsters, each of them 300x300 pixels large, plus 300 bullets, each of them 10x10 pixels large, animated at least 20 frames per second. Now you have something to be measured. And the answer would be that it requires computer with processor speed X and memory Y to do that.
If the number is realistic, just do it. If the number is just a bit high, do it anyway... it will take you some time to complete the game, and meanwhile the computers will become at least twice faster.
If the number is too high, you might rethink your game. Is it really necessary to have 50 monsters on screen at the same time? Could they be smaller? Could we get some speed by avoiding partial transparency in bitmaps? Less particles in explosions? Etc. You probably can make some sacrifice.
I think you can do it. Remember, the computers are getting faster.
