For a typical weekend warrior in marginal condition yes, I dont know your level of conditioning so its always a guess. You have three tough days in row that are weather dependent without a lot of good options to bypass the summits. It could be spectacular as you are hitting some of he premier back packing trails in the park.
Day 2 (KSC to Russel) is a very long one even if you skip the summit via the cut off trail We went from Davis Pond to KSC and ate up most of the day (but we took our time and the baxter peak cut off) Hauling a backpack up and over the boulders on the Hunt Trail can slow you down. The Northwests Basin trail is quite wet earlier in the season. Best done in late August/Early September. Day 3 is potentially spectacular but there is major crossing of Wassataquoik stream which has no bypass. Its down low on Northern Peaks trail not that far from where its splits off from the Northwest basin trail. We had to wade across it over our knees on Labor day weekend during a dry summer. Hard to beat the Howe Peaks, Hamlin and hiking down Hamlin Ridge trail. Its rarely traveled, you may not see anyone until Hamlin probably one of the most remote above treeline stretches in the Northeast
Keep in mind for that on day four that the Dudley Trail is closed so there is no good option to do the Knife Edge unless you hike back down to Roaring Brook to catch the Helon Taylor trail. If you really want to do it your best option is Cathedral trail up to the summit and then do an out and back along the Knife Edge to Pamola.
Its a very aggressive schedule for most folks with one long day followed by two tough days. You are very dependent on good weather. Treeline is lower than in the whites or the ADK and the summit plateau is longer. All three days require 3 to 4 hours of full exposure with little or no cover. The mountain tends to attract afternoon storms but your itinerary means you may be up there in the early afternoon. Best option is adopt an early wakeup every morning to get up above treeline early. During the summer there can be persistent high pressure systems that hang around for a week at a time but sometimes the weather is in 3 1/2 day pattern with rain on the third day. If the weather goes bad you may have to head down to a road to avoid the summits and hitch a ride back to KSC. Hitching usually isnt a major issue as there are a lot of campers and day hikers heading where you need to go.
Some minor planning items
KSC is a pretty densely spaced campground (for BSP) unless you are on the south side of the stream you will have neighbors. The park has quiet hours but with lots of families it can be bit noisy at times. The critters are very agressive, keep all food in the trunk. Russell Pond and Chimney Pond have a unusual bear line design, bring a good bag for hanging food.
The water source to Russell Pond is the pond and it has a decided boggy taste. I expect a filter is preferable to chemical treatment and suggest some flavoring.
If you hit a good stretch of weather this is going to trip to remember, there is nothing like it in the whites or the ADKs. Once you get away from the day hikers and head north of the summit you will see few folks.
Car navigation systems really do not like the park and will attempt to have you drive over old logging roads that are now trails or havent been roads for 50 years. Some dont recognize the Togue Pond gatehouse and route you to the Park Headquarters in Millinocket. Bring a map. There are several good hiking trail maps of the park. Some are out of date. The headquarters has variety and there is also a welcome center just before the gatehouse that is normally open and sell the same maps.
A general observation is folks heading to Baxter tend to under estimate how long it takes to get there. Its a long drive from anywhere and once you are in Millinocket your trip is not over. The trip to park gate can take 45 minutes and the drive from the Togue Pond gatehouse to KSC can take another 45 minutes. There is small well stocked grocery store in Millinocket and plenty of spots to buy ice, one you leave ton and go under the railroad bridge there is only one more camp store that runs on a generator and you pay for the convenience.