Sort of, within limits . HDPE and LDPE melt at temperatures that won't damage silicone designed for that temperature (some silicones that are designed for lower temperature ranges can degrade from the heat). However, HDPE and LDPE don't turn into a liquid. They're more like sticky putty or dense taffy. They don't flow nicely into fine detail; you need to force it into the detail. Also, the plastic shrinks as it cools and it's very hard to cool it perfectly uniformly. So it warps a lot, and with a lot of force.
With a metal mold, you can force the melted plastic into the mold detail with some pressure without distorting the mold. You can control the cooling and keep it under a lot of pressure as it cools so it doesn't warp.
DIYers often just make blanks of plastic that can be cut into shape and machined. You can use something like a simple wooden mold lined with oven parchment paper or a non-stick metal pan. Once the plastic is melted, it is covered with a solid piece that acts like a piston, and clamps are used to compress the plastic flat in the mold. As the plastic is forced into the nooks and crannies, and cools and shrinks, you periodically tighten the clamps. When the plastic is completely cool, it's typically a reasonably flat plastic blank with some excess that squeezed out around the edges. That gets trimmed away, leaving a flat piece of plastic stock. That's not exactly what you want to do, but that process will give you an idea of what it takes to produce a molded plastic piece with this material.
The problem with silicone is that it's very flexible. For a simple shape, you can make a firm silicone mold that is reinforced with an external shell to keep the shape from distorting too much. But any small detail will distort under the pressure needed to get a good casting, or via warpage as the plastic cools.
I've made molds for things like reasonably thin HDPE brackets out of wood and lined it with a film of thinned silicone so the plastic didn't stick to it. That worked fine. If what you want to mold has a significant thickness, it will be a challenge to get an accurate result using a silicone mold.
If the item is thick and has some detail, what might work better, although I haven't tried it with HDPE or LDPE, is casting the mold out of something like casting cement (a fine material that preserves surface detail). Use as many sections as necessary so the mold can be disassembled without damage after using it to make your item, and support that inside something like a wooden box so all of the pressure is compressive force on the cement. You will probably need some form of mold release.
I've seen a video of a somewhat similar method used to cast a slingshot body. The shape was replicated on a bunch layers of corrugated cardboard that were duct-taped together to create the needed thickness. This was put in a wooden frame and regular concrete was poured around it. When the concrete hardened, the mock-up was removed.
To mold the HDPE, the concrete mold was laid on a piece of oven parchment paper on a cookie sheet. The cavity was filled with bits of plastic and the whole thing went in the oven. As the plastic melted, more was added, pressing the melted plastic into the nooks and crannies until the cavity was full. It was cooled without any kind of compression.
The result was a bit crude. The concrete broke up removing the casting, and the casting required a lot of cleanup to get some of the surfaces smooth and uniform. But the end result looked pretty good. Cutting the shape out of a flat plastic blank would have been less work, but it demonstrates that cement can work as a mold for a thick HDPE item.