In the E visa context, this is what the govt says:
An applicant for an E visa need not establish intent to proceed to the United States for a specific temporary period of time. Nor does an applicant for an E visa need to have a residence in a foreign country which the applicant does not intend to abandon. The alien may sell his or her residence and move all household effects to the U.S. The alien's expression of an unequivocal intent to return when the E status ends is normally sufficient, in the absence of specific indications of evidence that the alien's intent is to the contrary. If there are such objective indications, inquiry is justified to assess the applicant's true intent. As discussed in 9 FAM 41.54 N4, an applicant might be a beneficiary of an immigrant visa petition filed on his or her behalf. However, the alien might satisfy the consular officer that his and/or her intent is to depart the United States upon termination of status, and not stay in the United States to adjust status or otherwise remain in the United States regardless of legality of status.
L aliens are specifically excluded from the intending immigrant presumption of section 214(b) of the INA and are, furthermore, not required to have a residence abroad which they have no intention of abandoning. In addition, INA 214(h) provides the fact that an alien has sought permanent residence in the United States does not preclude him or her from obtaining an L nonimmigrant visa (NIV) or otherwise obtaining or maintaining that status. The alien may legitimately come to the United States as a nonimmigrant under the L classification and depart voluntarily at the end of his or her authorized stay, and, at the same time, lawfully seek to become a permanent resident of the United States. Consequently, the consular officer's evaluation of an applicant's eligibility for an L visa shall not focus on the issue of temporariness of stay or immigrant intent.
By law, L-1 and H-1 holders are PERMITTED by the doctrine of dual intent to have their green cards pending. This is beyond question. That your green card application is pending can never be a ground for denial of your H or L visa application (includes H-4 and L-2).
As I have noted above, E-1, E-2 visas have an unclear situation. It appears the consulates WILL permit them dual intent, but may not(???). They do NOT have the same level of protection as H and L visas but usually consulates will permit dual intent.
The following visa types have no such protection and their vise or entry into USA can be denied if they have a green card application application in process: B-1, B-2, F-1/F-2, J-1, J-2.
O-1 is allowed to have an immigrant intent (by regulations - though not by statute).
Pursuant to 8 CFR Section 214.2(O)(13)
(13) Effect of approval of a permanent labor certification or filing of a preference petition on O classification. The approval of a permanent labor certification or the filing of a preference petition for an alien shall not be a basis for denying an O-1 petition, a request to extend such a petition, or the alien's application for admission, change of status, or extension of stay. The alien may legitimately come to the United States for a temporary period as an O-1 nonimmigrant and depart voluntarily at the end of his or her authorized stay and, at the same time, lawfully seek to become a permanent resident of the United States.
TN is also not allowed dual intent, but are often not questioned on their green card pendency.