It does not. Immortality type 9, AE, Acausality type 3, etc. These abilities have nothing to do with regeneration and are completely independent of the entity being erased from existence as their immortality is always related to an outside factor. The NLF is you saying EE would by default bypass these.
Sure I agree, it doesn't bypass AE etc... by default (unless it does have the interaction but AE type 2 is still interactive, since this in this notion a character have a physical form but just embodies an abstraction) and in this instance, Dogi Dogi's time power can interact with her and it has this;
Existence Erasure (Passive & Active; History & Information [Type 2]; Time Power can create, sustain, and also erase Time,[67][64][68][69][70][71] with history, past, present, future, flow of time, flow of eventscausality & fate[30][16][31][32][33][34][35][36][37][38][12][39][40] all being a part of Time. Time Power can even passively erase others from existence,[51] completely remove them from history, make them vanish without a trace like they never existed, forever forgotten;[52] Stated to be capable of erasing everything,[69][124] removing all of existence[33] & even[125] entire histories[126] completely[127]. Can erase abstract beings such as Infinite Zamasu (Game) who became the very will/thoughts of justice and merged with the fabric of the universe,[93][99][100][39][93][99][100] and reduce existence itself to a state of zero.[20] Time Energy, which is the basis of Time Power, is an all-encompassing energy that creates, composes and sustains time, thus the energy itself[128] is also capable of destroying everything across time, erasing all of existence, the entire multiverse from history.[87][28][85][87][129][130][88] Time Power's erasure is one of the strongest erasure powers in the verse, as it is capable of erasing[131][132] the entire cosmology, all histories and everything they contain, including special space-times such as the Ziku World which is comprised purely from WiFi Network Data and Information; beings like Dr. Mashirito, Arale, Gatchan whom resisted narrative erasure[133] that includes data & information erasure and beings who resist Power of Destruction such as Gods of Destruction,[134] Frieza, etc. As the power that created the Time Scrolls, it can erase Time Scrolls completely along with the recorded data and information of histories contained within those scrolls. It can also erase the recorded data and information directly while leaving behind an unharmed blank scroll[9])
Time power can interact with these;
Ghosts, Spirits, Soul, Illusions, Energy, Invisibility, Intangibility (Elemental, Immaterial & Phasing), Incorporeality & Abstractions (Will, Thoughts, Ideas & Emotions; Upscales to Dragon Ball Heroes Multiverse's Ki which is also an energy-type power like Time Power, which can interact with ghosts, spirits, souls, illusions, pure energy beings, invisible and intangible ki blasts, abstract wills, thoughts, ideas, emotions,[91][92][93][94][95][96][97][98][21][93][99][100][39] As a power that creates and controls time, the entire multiverse and all histories/space-time/timelines, Time Power can affect everything including Infinite Zamasu (Game) who became the very will, thoughts of justice and merged with the fabric of the universe.[93][99][100][39] Can interact with its own attacks which can take the form of flame, lighting or simply being pure energy blast)
Data & Information (Type 2; Scales to Dragon Ball Heroes Multiverse's Ki which is also an energy-type power like Time Power, which can interact[102] with the Ziku World which is a digital space-time comprised purely from WiFi Network Data and Information. Time Power is stated to be able to control and erase all space-times, the entire multiverse which includes the Ziku World itself which is also a space-time within the multiverse. Can affect recorded data and information of history in the Time Scrolls, these Time Scrolls themselves are also just a manifestation of Time Power.)
So yeah, in this instance Fu summoning Dogi Dogi is just a win for him + 6 layers on top of that, Even without Dogi Dogi.. There's so many ways that Fu still incaps her on end. Since this is interactive;
Abstract Existence (
Type 1: Energy,
Emotions,
Thoughts,
Information [
Type 2])
Fu himself has Enhanced Causality (superior than Dark Demon god power, which is also superior to Dark ki)/Fate hax
Enhanced Causality Manipulation & Fate Manipulation (Superior to Demon God Power which in turn is far superior to Dark Ki, the Dark Factor is stated to be able to rule Time[75][76] with time, fate & history all being the same thing due to the past, present & future being the pieces that comprise them all.[81][82][2][83][76][84][85][86][58][57][60][30][87][88][89][90] Also stated to have complete control[91] over all of past, present, future, time and space.[84])